the steady motion of a navier stokes liquid around a rigid body let mathcal r be a body moving by prescribed rigid motion in a navier stokes liquid mathcal l that fills the whole space and is subject to given boundary conditions and body force under the assumptions that with respect to a frame mathcal f attached to mathcal r these data are time independent and that their magnitude is not too large we show the existence of one and only one corresponding steady motion of mathcal l with respect to mathcal f such that the velocity field at the generic point x in space decays like x 1 these solutions are physically reasonable in the sense of finn 10 in particular they are unique and satisfy the energy equation among other things this result is relevant in engineering applications involving orientation of particles in viscous liquid 14

partial regularity of a generalized solution to the navier stokes equations in exterior domain in this note we prove two regularity theorems for solutions to the navier stokes equations of an i b v p in exterior domains namely we prove that the sets of the singular points of a solution if not empty has at most 1 hausdorff measureh1 s 0 moreover the sets is enclosed in a sphere of rayr for anyt 0 these results are obtained as corollaries to the partial regularity results furnished in 2

existence uniqueness and l q estimates for the stokes problem in an exterior domain as is well known the study of the properties of solutions to the stokes system plays an essential role in the mathematical theory of viscous fluid flows governed by the navier stokes equations it is not art overstatement to say that existence uniqueness and a priori estimates in sobolev spaces for the stokes system are fundamental in every basic question related to the navier stokes equations such as existence regularity asymptotic behavior in time etc see e g ladyzhenskaya 1969 solonni ov 1977 and te am 1977 so far however the stokes system has been fully analyzed only for bounded domains see sobolevskn 1960 ladvznenskaya 1959 solonnu ov 1960 vorovlch yot oowcr 1961 cattabrma 1961 in particular in the paper of cattabriga a complete treatment is given in the sobotev spaces w l 1 1 q c for space dimension n 3 cattabriga s results essentially state that if 2 is a bounded domain in r a of class c m m max l 2 2 l 1 then given f e wt q y2 3 gc wt l q o q e wl 2 1 q q 8o a 1 q there exists one and only one distributional solution v c w1 z q q 3 p e wt l q o to the stokes system

decomposition of besov and triebel lizorkin spaces on the sphere abstract a discrete system of almost exponentially localized elements needlets on the n dimensional unit sphere s n is constructed it shown that the needlet system can be used for decomposition of besov and triebel lizorkin spaces on the sphere as an application of besov spaces on s n a jackson estimate for nonlinear m term approximation from the needlet system is obtained

non homogeneous generalized newtonian fluids we show the existence of weak solutions to the system describing the motion of incompressible non homogeneous generalized newtonian fluids if the extra stress tensor s d possesses p structure with p ge frac 3d 2 d 2 and variable viscosity the limiting process in the equation of motion is justified by a variational argument which is new in this context

multiresolution analysis and adaptive estimation on a sphere using stereographic wavelets abstract we construct an adaptive estimator of a density function on d dimensional unit sphere s d d 2 using a new type of spherical frames the frames or as we call them stereografic wavelets are obtained by transforming a wavelet system namely daubechies using some stereographic operators we prove that our estimator achieves an optimal rate of convergence on some besov type class of functions by adapting to unknown smoothness our new construction of stereografic wavelet system gives us a multiresolution approximation of l 2 s d which can be used in many approximation and estimation problems in this paper we also demonstrate how to implement the density estimator in s 2 and we present a finite sample behavior of that estimator in a numerical experiment

characterizations of function spaces on the sphere using frames in this paper we introduce a polynomial frame on the unit sphere s d 1 of r d for which every distribution has a wavelet type decomposition more importantly we prove that many function spaces on the sphere s d 1 such as l p h p and besov spaces can be characterized in terms of the coefficients in the wavelet decompositions as in the usual euclidean case r d we also study a related nonlinear m term approximation problem on s d 1 in particular we prove both a jackson type inequality and a bernstein type inequality associated to wavelet decompositions which extend the corresponding results obtained by r a devore b jawerth and v popov compression of wavelet decompositions amer j math 114 1992 no 4 737 785

monotonic decreasing and asymptotic behavior of the kinetic energy for weak solutions of the navier stokes equations in exterior domains existence of weak solutions of the three dimensional navier stokes problem was first proved by j leray in the case of the cauchy problem cf leray 1934 as is well known these solutions are important in that they are the only solutions which so far are known to exist for all times without restriction on the data unfortunately however the question of whether they are classical in an ordinary sense is still open even though partial conclusions regarding regularity are avilable leray 1934 scheffer 1976 1980 caffarelli kohn nirenberg 1982 subsequently e hopf 1951 using a different technique constructed weak solutions for a general initial boundary value problem however hopf s solution even for the cauchy problem has weaker properties than leray s solution among others we refer to the energy inequality for the velocity field u x t i e ntimits mega u 2 x t dx ntimits mega u 2 x s sx eqq 2ntimits s t ntimits mega abla u abla udxdau i for s 0 for almost all s 0 and for all t s

on energy inequality smoothness and large time behavior in l 2 for weak solutions of the navier stokes equations in exterior domains soit un domaine exterieur de r n n 3 4 a frontiere lisse sur le cylindre d espace temps 0 on considere le probleme de navier stokes non stationnaire u t u u u p f dans 0 u 0 dans 0 u 0 sur 0 u x 0 a x avec des donnees prescrites f et a

disturbance decoupling for linear time invariant systems a matrix pencil approach we give a new systematic analysis of disturbance decoupling problems for standard linear time invariant systems based on the theory of matrix pencils this approach is based on the computation of condensed forms under orthogonal equivalence transformations from these forms which can be computed in a numerically stable way we obtain new necessary and sufficient conditions that are numerically verifiable and furthermore we immediately obtain numerically stable algorithms to compute the desired compensators we present a numerical example that demonstrates the properties of the new approach

inclusion principle for linear time varying systems the main objective of this paper is to consider time varying linear systems within the framework of the inclusion principle starting from general definitions conditions are derived for a dynamic system to include a dynamic system of smaller dimension particular attention is paid to restriction and aggregation the most important special cases of inclusion it is proved using geometric arguments within the general time varying context that any inclusion relationship on a given time interval can be decomposed into a sequence of restriction aggregation pairs connections between inclusion and zero state equivalence are discussed the paper also presents a formulation of the contractibility expandability conditions for time varying state feedback controllers

concentration inequalities and confidence bands for needlet density estimators on compact homogeneous manifolds let x 1 x n be a random sample from some unknown probability density f defined on a compact homogeneous manifold m of dimension d 1 consider a needlet frame phi j eta describing a localised projection onto the space of eigenfunctions of the laplace operator on m with corresponding eigenvalues less than 22j as constructed in geller and pesenson j geom anal 2011 we prove non asymptotic concentration inequalities for the uniform deviations of the linear needlet density estimator f n j obtained from an empirical estimate of the needlet projection sum eta phi j eta int f phi j eta of f we apply these results to construct risk adaptive estimators and nonasymptotic confidence bands for the unknown density f the confidence bands are adaptive over classes of differentiable and holder continuous functions on m that attain their holder exponents

boundary layer phenomena for the boundary layer for the heat conductive incompressible viscous fluids in the half space abstract this paper is concerned with the initial boundary value problem of the heat conductive viscous fluid in r 2 we prove the convergence rate of the solutions as the heat diffusive coefficient k goes to zero using some uniform in k estimates moreover the thickness of the boundary layer is obtained and the boundary layer solution is constructed to describe the behavior of boundary layers

asymptotic behavior and time discretization analysis for the non stationary navier stokes problem the asymptotic behavior and the euler time discretization analysis are presented for the two dimensional non stationary navier stokes problem if the data and f t satisfy a uniqueness condition corresponding to the stationary navier stokes problem we then obtain the convergence of the non stationary navier stokes problem to the stationary navier stokes problem and the uniform boundedness stability and error estimates of the euler time discretization for the non stationary navier stokes problem

on the global existence and convergence to steady state of navier stokes flow past an obstacle that is started from rest a new approach to the existence theory for the navier stokes equations using a technique of kato 15 further developed in combination with estimates for oseen s equation by kobayashi shibata 17 and shibata 24 has made possible the solution of a long standing open problem often referred to as finn s starting problem this paper provides the solution

a uniqueness theorem for viscous fluid motions in exterior domains as is known one of the most interesting still open questions in the dynamics of viscous incompressible flows governed by the navier stokes equations is that of the uniqueness of three dimensional motions an early answer to this problem is found in the paper 5 of e fo subsequently the uniqueness question acquired new importance when it was recognized by j leray 18 that when formulated in a suitable class it is tightly linked with that of the existence of global in time and regular solutions to the navier stokes equations el also 17 22 23 the above class is called the hopf class which consists of those weak solutions satisfying suitable summability conditions along with the energy inequality in particular they and their first spatial derivatives belong to the lebesgue space l2 2 q is the domain of motion however it was also recognized by j kamp de f riet that in general an existence and uniqueness theory in l2 classes is not well suited to studying homogeneous turbulence 16 when q is unbounded motivated by these and other considerations d graffi in a remarkable paper of 1960 13 proved uniqueness for classical solutions in an arbitrary smooth unbounded domain without assuming that the velocity field v tends to a limit at infinity rather he required v and vv only bounded in space and time however he needed suitable assumptions on the behavior of the pressure p at infinity this type of problem has been reconsidered by several authors who improved graffi s theorem by reducing the assumptions on both v and p but who still required that the pressure tends to a limit po suitably at great distances 2 4 6 12 21 26 actually it is worth remarking that one of the main goals of papers 3 4 8 21 was just to avoid or at least to weaken as far as possible the hypothesis about p po for such an assumption is always an undesired feature for flows of incompressible fluids this kind of results which hold for

contractibility of dynamic lti controllers using complementary matrices a generalized structure of complementary matrices involved in the input state output inclusion principle for linear time invariant systems including contractibility conditions for static state feedback controllers is well known in this note it is shown how to further extend this structure when considering contractibility of dynamic controllers necessary and sufficient conditions for contractibility are proved in terms of both unstructured and block structured complementary matrices for general expansion contraction transformation matrices explicit sufficient conditions for blocks of complementary matrices ensuring contractibility are proved for general expansion contraction transformation matrices moreover these conditions are further specialized for a particular class of transformation matrices

generalized selection of complementary matrices in the inclusion principle this paper presents a strategy for choosing complementary matrices in the framework of the inclusion principle with state lq optimal control of lti systems it is based on translating the basic restrictions given by the inclusion principle into explicit block structures for these matrices the degree of freedom given by these structures is illustrated by means of an example of overlapping decentralized control design

feedback design for regularizing descriptor systems this paper surveys numerical techniques for the regularization of descriptor generalized state space systems by proportional and derivative feedback we review generalizations of controllability and observability to descriptor systems along with definitions of regularity and index in terms of the weierstras canonical form three condensed forms display the controllability and observability properties of a descriptor system the condensed forms are obtained through orthogonal equivalence transformations and rank decisions so they may be computed by numerically stable algorithms in addition the condensed forms display whether a descriptor system is regularizable i e when the system pencil can be made to be regular by derivative and or proportional output feedback and if so what index can be achieved also included is a a new characterization of descriptor systems that can be made to be regular with index 1 by proportional and derivative output feedback

decentralized estimation and control with overlapping input state and output decomposition abstract the extension principle which was introduced recently is generalized to the case of input state and output expansion estimator and controller design problems are considered within the framework of the extension principle decentralized estimator and controller design with overlapping decompositions is also discussed within the same framework it is shown that if the extension principle is used then any estimator or controller designed in the expanded spaces is contractible to the original spaces for implementation furthermore it is shown that if an estimator designed for the expanded system achieves good estimation and or asymptotic estimation then the contracted estimator also achieves good estimation and or asymptotic estimation for the original system similarly it is also shown that if a controller designed for the expanded system achieves stability and or good performance then the contracted controller achieves stability and or good performance for the original system

global weak solutions for the two dimensional motion of several rigid bodies in an incompressible viscous fluid we consider the two dimensional motion of several non homogeneous rigid bodies immersed in an incompressible non homogeneous viscous fluid the fluid and the rigid bodies are contained in a fixed open bounded set of r 2 the motion of the fluid is governed by the navier stokes equations for incompressible fluids and the standard conservation laws of linear and angular momentum rule the dynamics of the rigid bodies the time variation of the fluid domain due to the motion of the rigid bodies is not known a priori so we deal with a free boundary value problem the main novelty here is the demonstration of the global existence of weak solutions for this problem more precisely the global character of the solutions we obtain is due to the fact that we do not need any assumption concerning the lack of collisions between several rigid bodies or between a rigid body and the boundary we give estimates of the velocity of the bodies when their mutual distance or the distance to the boundary tends to zero

existence and regularity of a class of weak solutions to the navier stokes equations abstract we construct a class of weak solutions to the navier stokes equations which have second order spatial derivatives and one order time derivatives of p power summability for 1 p 5 4 meanwhile we show that u l s 0 t w 2 r with 1 s 3 2 r 2 for 1 r 5 4 r can be relaxed not to exceed 3 2 if we consider only in the interior of in the end we extend the classical regularity theorem our results show that u is a regular solution if u l s 0 t l r with 1 s 3 2 r 1 for satisfying 1 3 with 1 s 1 r 5 6 for arbitrary domain in r 3 and 1 s 2 for r n with n 3 this result was previously obtained byh beirao da veiga chinese ann math ser b 16 1995 407 412

asymptotic behavior for the navier stokes equations in 2d exterior domains we show that the lp spatial temporal decay rates of solutions of incompressible flow in an 2d exterior domain when a domain has a boundary pressure term makes an obstacle since we do not have enough information on the pressure term near the boundary to overcome the difficulty we adopt the ideas in he xin c he z xin weighted estimates for nonstationary navier stokes equations in exterior domain methods appl anal 7 3 2000 443 458 and our previous results h o bae b j jin asymptotic behavior of stokes solutions in 2d exterior domains j math fluid mech in press h o bae b j jin temporal and spatial decay rates of navier stokes solutions in exterior domains submitted for publication for the spatial decay rate estimate we first extend temporal decay rate result of the navier stokes solutions for general lp space when the initial velocity is in l 2 lr 1 r q 1 r q

finite element approximation for the viscoelastic fluid motion problem in this article the variational formulation of the two dimensional viscoelastic fluid motion problem and its finite element approximation are considered an local error estimate for the velocity with h1 norm and the pressure with l2 norm is obtained and a uniform error estimate for the velocity and pressure with the above norms is provided if the given data satisfies the uniqueness condition

rates of contraction for posterior distributions in lr metrics 1 r the frequentist behavior of nonparametric bayes estimates more specifically rates of contraction of the posterior distributions to shrinking lr norm neighborhoods 1 r of the unknown parameter are studied a theorem for nonparametric density estimation is proved under general approximation theoretic assumptions on the prior the result is applied to a variety of common examples including gaussian process wavelet series normal mixture and histogram priors the rates of contraction are minimax optimal for 1 r 2 but deteriorate as r increases beyond 2 in the case of gaussian nonparametric regression a gaussian prior is devised for which the posterior contracts at the optimal rate in all lr norms 1 r

an inclusion principle for dynamic systems the purpose of this paper is to present a detailed study of the inclusion concept in dynamic systems which is a suitable mathematical framework for comparing systems with different dimensions the framework offers immediate results in reduced order modeling and the overlapping decentralized control of complex systems the presentation which is limited to linear constant systems relies on both the matrix algebra computations and the geometric elements structure to provide a balanced view of the issues involved in the concept of inclusion the framework is quite broad and has been used to consider nonlinear and time varying systems as well as systems with hereditary and stochastic effects

localized spherical deconvolution we provide a new algorithm for the treatment of the deconvolution problem on the sphere which combines the traditional svd inversion with an appropriate thresholding technique in a well chosen new basis we establish upper bounds for the behavior of our procedure for any l p loss it is important to emphasize the adaptation properties of our procedures with respect to the regularity sparsity of the object to recover as well as to inhomogeneous smoothness we also perform a numerical study which proves that the procedure shows very promising properties in practice as well

inclusion principle for descriptor systems the purpose of this paper is to propose an expansion contraction framework for linear constant descriptor systems within the inclusion principle for dynamic systems our primary objective is to provide an explicit characterization of the expansion process whereby a given descriptor system is expanded into the larger space where all its solutions are reproducible by the expanded descriptor system if appropriate initial conditions are selected when a control law is formulated in the expanded space the proposed characterizations provide contractibility conditions for implementation of the control law in the original system a full freedom is provided for selecting appropriate matrices in the proposed expansion contraction control scheme in particular the derived theoretical framework serves as a flexible environment for expansion contraction control design of descriptor systems under overlapping information structure constraints

micro motions of a 2 d swimming model governed by multiplicative controls abstract the goal of this paper is to derive a formula for the micro motions of a simplified model of an object swimming by itself in a 2 d stokes fluid mathematics wise the model equations are described by a nonlinear coupled hybrid system of fluid equations and integro differential equations we view this swimming motion as one governed by multiplicative controls such problems are of interest in biological and engineering applications dealing with propulsion systems in fluids

solutions for semilinear parabolic equations in lp and regularity of weak solutions of the navier stokes system abstract we construct a unique local regular solution in l q 0 t l p for a class of semilinear parabolic equations which includes the semilinear heat equation u t u u u 0 and the navier stokes system here p and q are so chosen that the norm of l q 0 t l p is dimensionless or scaling invariant the main relation between p and q for the semilinear heat equation is 1 q 1 p 1 q n 2 provided that initial data are in l r with r n 2 1 where n is the space dimension applying our regular solutions to the navier stokes system we show that the k 2 dimensional hausdorff measure of possible time singularities of a turbulent solution is zero if the turbulent solution is in l q 0 t l p where k 2 q nq p p n 1 q we show moreover that a turbulent solution is regular if it is in c 0 t l n

minimum norm regularization of descriptor systems by mixed output feedback we study the regularization problem for linear constant coefficient descriptor systems ex ax bu y1 cx y2 x by proportional and derivative mixed output feedback necessary and sufficient conditions are given which guarantee that there exist output feedbacks such that the closed loop system is regular has index at most one and e bg has a desired rank i e there is a desired number of differential and algebraic equations to resolve the freedom in the choice of the feedback matrices we then discuss how to obtain the desired regularizing feedback of minimum norm and show that this approach leads to useful results in the sense of robustness only if the rank of e is decreased numerical procedures are derived to construct the desired feedback gains these numerical procedures are based on orthogonal matrix transformations which can be implemented in a numerically stable way

on weighted norm estimates for nonstationary incompressible navier stokes flows in a 3d exterior domain abstract we study the time decay of weighted norms of weak and strong solutions to the navier stokes equations in a 3d exterior domain moment estimates for weak solutions and weighted l q estimates for strong solutions are deduced both of which seem to be optimal the relation is discussed between the space time decay and the vanishing of the total net force exerted by the fluid to the body a class of initial data is given so that the total net force associated to the corresponding fluid flows does not vanish

the smoothness test for a density function abstract the problem of testing hypothesis that a density function has no more than derivatives versus it has more than derivatives is considered for a solution the l 2 norms of wavelet orthogonal projections on some orthogonal differences of spaces from a multiresolution analysis is used for the construction of the smoothness test an asymptotic distribution of a smoothness estimator is used to analyze that asymptotic distribution a new technique of enrichment procedure is proposed the finite sample behavior of the smoothness test is demonstrated in a numerical experiment in case of determination if a density function is continuous or discontinuous

contractibility of overlapping decentralized control abstract the purpose of this paper is to generalize the concept of contractibility of decentralized control laws in the inclusion principle after a system with overlapping subsystems is expanded into a larger space and decentralized control laws are formulated for the disjoint subsystems the laws need to be contracted for implementation in the original space we propose broader definitions of restriction and aggregation in the framework of inclusion which provide more flexibility in the contraction phase of the expansion contraction process in particular we discuss contractibility conditions for dynamic output controllers including state observers which have been of special interest in applications

controllability of the semilinear parabolic equation governed by a multiplicative control in the reaction term a qualitative approach in this paper we are concerned with the global nonnegative approximate controllability property of a rather general semilinear heat equation with superlinear term governed in a bounded domain omega subset r n by a multiplicative bilinear control in the reaction term like v u x t where v is the control we show that any nonnegative target state in l 2 omega can approximately be reached from any nonnegative nonzero initial state by applying at most three static bilinear l infty omega controls subsequently in time this result is further applied to discuss the controllability properties of the nonhomogeneous version of this problem with bilinear term like v u x t theta x where theta is given our approach is based on an asymptotic technique allowing us to distinguish and make use of the pure diffusion and or pure reaction parts of the dynamics of the system at hand while suppressing the effect of a general nonlinear term

local controllability for a swimming model we study the local controllability of a mathematical model of an abstract object which swims in the two dimensional 2d nonstationary stokes fluid we assume that this object consists of finitely many subsequently connected small sets thick points each of which can act upon any of the adjacent sets in a rotation fashion with the purpose of generating its fish or snake like motion we regard the magnitudes of the respective rotation forces entering the system s equations as coefficients as multiplicative or bilinear controls the structural integrity of the object is maintained by the elastic forces acting between the aforementioned adjacent sets according to hooke s law models like this are of a interest in biology and engineering applications dealing with propulsion systems in fluids

lp approach to steady flows of viscous compressible fluids in exterior domains we investigate steady compressible flows in three dimensional exterior domains for small data and for both zero and nonzero but constant velocity at infinity we prove existence and uniqueness of solutions in l p spaces p 3 and study their regularity as well as their decay at infinity

on the asymptotic behaviour of the l 2 norm of suitable weak solutions to the navier stokes equations in three dimensional exterior domains we provel2 decay rates of suitable weak solutions to the navier stokes equations in exterior domains the results for the order of decay are the same as for the solutions to the cauchy problem of the navier stokes equations finally in the case of r3 the decay rate order is sharp in the class of solutions considered by us

block threshold rules for curve estimation using kernel and wavelet methods motivated by recently developed threshold rules for wavelet estimators we suggest threshold methods for general kernel density estimators including those of classical rosenblatt parzen type thresholding makes kernel methods competitive in terms of their adaptivity to a wide variety of aberrations in complex signals it is argued that term by term thresholding does not always produce optimal performance since individual coefficients cannot be estimated sufficiently accurately for reliable decisions to be made therefore we suggest grouping coefficients into blocks and making simultaneous threshold decisions about all coefficients within a given block it is argued that block thresholding has a number of advantages including that it produces adaptive estimators which achieve minimax optimal convergence rates without the logarithmic penalty that is sometimes associated with term by term thresholding more than this the convergence rates are achieved over large classes of functions with discontinuities indeed with a number of discontinuities that diverges polynomially fast with sample size these results are also established for block thresholded wavelet estimators which although they can be interpreted within the kernel framework are often most conveniently constructed in a slightly different way

a class of solutions to stationary stokes and navier stokes equations with boundary data in w 1 q q we develop a theory for a general class of very weak solutions to stationary stokes and navier stokes equations in a bounded domain with boundary of class c2 1 corresponding to boundary data in the distribution space w 1 q q 1 q these solutions exist and are unique for small data in the nonlinear case in their class of existence and satisfy a correponding estimate in terms of the data moreover they become regular if the data are regular to our knowledge the only existence result for solutions attaining such boundary data is due to giga 16 proposition 2 2 for the stokes case however the methods and the approach used in the present paper are different than giga s and cover more general issues including the nonlinear navier stokes equations and the precise way in which the boundary data are attained by the solutions we also introduce in the last section a further generalization of the solution class

well posedness of 2 d and 3 d swimming models in incompressible fluids governed by navier stokes equations abstract we introduce and investigate the wellposedness of two models describing the self propelled motion of a small bio mimetic swimmer in the 2 d and 3 d incompressible fluids modeled by the navier stokes equations it is assumed that the swimmer s body consists of finitely many subsequently connected parts identified with the fluid they occupy linked by the rotational and elastic forces the swimmer employs the change of its shape inflicted by respective explicit internal forces as the means for self propulsion in a surrounding medium similar models were previously investigated in 15 16 17 18 19 where the fluid was modeled by the liner nonstationary stokes equations such models are of interest in biological and engineering applications dealing with the study and design of propulsion systems in fluids and air

model abstraction and inclusion principle a comparison this paper discusses connections between the inclusion principle and model abstraction in large scale hierarchical control systems it also provides conditions for implementation of controllability and observability in linear continuous time dynamic systems satisfying either aggregation or restriction conditions as well as for observability implementation in linear continuous time dynamic systems satisfying conditions for abstraction

on the energy inequality for weak solutions to the navier stokes equations of compressible fluids on unbounded domains abstract we consider the navier stokes equations of compressible isentropic viscous fluids on an unbounded three dimensional domain with a compact lipschitz boundary under the condition that the total mass of the fluid is finite we show the existence of globally defined weak solutions satisfying the energy inequality in differential form

on the blowup criteria and global regularity for the non diffusive boussinesq equations with temperature dependent viscosity coefficient abstract in this paper we consider the boussinesq equations with temperature dependent viscosity and zero thermal diffusivity a blowup criterion of classical solution depending only on l q 0 t l p with p 2 and 1 p 1 q 1 2 is obtained for the two dimensional equations this is in particular consistent with the results in chae 2006 hou and li 2005 lai et al 2011 where the global regularity of the 2d non diffusive boussinesq equations with constant viscosity coefficient i e const was proved a serrin s type blowup criterion depending on u l s 0 t l r l q 0 t l p with r p 3 3 r 2 s 1 and 3 p 2 q 1 is obtained for the three dimensional case we also study the global regularity with large data for the two dimensional equations in a non divergence form

adaptive confidence sets in l 2 the problem of constructing confidence sets that are adaptive in l 2 loss over a continuous scale of sobolev classes of probability densities is considered adaptation holds where possible with respect to both the radius of the sobolev ball and its smoothness degree and over maximal parameter spaces for which adaptation is possible two key regimes of parameter constellations are identified one where full adaptation is possible and one where adaptation requires critical regions be removed techniques used to derive these results include a general nonparametric minimax test for infinite dimensional null and alternative hypotheses and new lower bounds for l 2 adaptive confidence sets

further properties of steady state solutions to the navier stokes problem past a three dimensional obstacle we show that the weak formulation of the steady state navier stokes problem in the exterior of a three dimensional compact set closure of a bounded domain corresponding to a nonzero velocity at infinity and subjected to a given body force is equivalent to a nonlinear equation in appropriate banach spaces we thus show that the relevant nonlinear operator enjoys a number of fundamental properties that allow us to derive many significant results for the original problem in particular we prove that the manifold constituted by the pairs u with the nondimensional speed at infinity reynolds number and u weak solution corresponding to and to a given body force f is for generic f a c one dimensional manifold and that for almost any the number of solutions is finite we also show that for any given f in the appropriate function space and any given 0 the corresponding solutions can be controlled by their specification only in a suitable neighborhood i of the boundary the size

inertial effects in small amplitude swimming of a finite body abstract we study the mechanism of small amplitude swimming of a deformable body of finite size in a viscous incompressible fluid described by the navier stokes equations the theory is based on a perturbation expansion in powers of the amplitude of surface displacements a nonvanishing swimming velocity is found in second order perturbation theory the average motion may include both a translational and a rotational contribution for harmonic time variation of the first order flow we are led to a natural definition of the efficiency of swimming

control at a distance of the motion of a rigid body immersed in a two dimensional viscous incompressible fluid abstract we consider the motion of a rigid body immersed in a two dimensional viscous incompressible fluid with navier slip with friction conditions at the solid boundary the fluid solid system occupies the whole plane we prove the small time global exact controllability of the position and velocity of the solid when the control takes the form of a distributed force supported in a compact subset with nonvoid interior of the fluid domain away from the body the strategy relies on the introduction of a small parameter we consider fast and strong amplitude controls for which the navier stokes rigid body system behaves like a perturbation of the euler rigid body system by the means of a multi scale asymptotic expansion we construct a controlled solution to the navier stokes rigid body system thanks to some controlled solutions to euler rigid body type systems and by using that the influence of the boundary layer on the solid motion turns out to be sufficiently small

the generalized eigenstructure problem in linear system theory the algebraic theory of linear time invariant systems has been studied in large detail during the past few decades and numerous computational algorithms have been developed to solve problems arising in this context in this paper the numerical aspects of a certain class of such algorithms dealing with what the author calls generalized eigenstructure problems are discussed some new and or modified algorithms are presented both the nmnerical stability of the algorithms and the conditioning of the problems they solve are analyzed using numerical criteria

decay estimates of gradient of a generalized oseen evolution operator arising from time dependent rigid motions in exterior domains let us consider the motion of a viscous incompressible fluid past a rotating rigid body in three dimensions where the translational and angular velocities of the body are prescribed but time dependent in a reference frame attached to the body we have the navier stokes system with the drift and one half of the coriolis terms in a fixed exterior domain the existence of the evolution operator t t s in the space l q generated by the linearized non autonomous system was proved by hansel and rhandi j reine angew math 694 1 26 2014 and the large time behavior of t t s f in l r for t s rightarrow infty was then developed by hishida math ann 372 915 949 2018 when f is taken from l q with q leqq r the contribution of the present paper concerns such l q l r decay estimates of nabla t t s with optimal rates which must be useful for the study of stability attainability of the navier stokes flow in several physically relevant situations our main theorem completely recovers the l q l r estimates for the autonomous case stokes and oseen semigroups those semigroups with rotating effect in three dimensional exterior domains which were established by hishida and shibata arch ration mech anal 193 339 421 2009 iwashita math ann 285 265 288 1989 kobayashi and shibata math ann 310 1 45 1998 maremonti and solonnikov ann sc norm super pisa 24 395 449 1997 and shibata in amann arendt hieber neubrander nicaise von below eds functional analysis and evolution equations the gunter lumer volume birkhauser basel pp 595 611 2008

contractible controller design and optimal control with state and input inclusion abstract a new inclusion concept which involves both state and input expansion is introduced it is shown that with the approach undertaken here any control law designed in the expanded spaces is always contractible to the original spaces the inclusion of the cost functions is also discussed and necessary and sufficient conditions are derived it is shown that unlike the case when the two input spaces are identical the inclusion conditions must in general depend on the control laws however certain sufficient conditions which do not involve final control laws can be found if the inclusion is taken with respect to the optimal control finally controller design with overlapping decompositions is discussed within the framework of the new inclusion concept and optimal control

decay rate of solutions of navier stokes equations in 3 dimensional half space abstract in this article we derive the l 2 spatial decay rate of a weak solution of the incompressible flow in the half space when the half space or some other fluid region with boundary is concerned pressure estimate is main obstacle since we do not have enough information of the pressure on the boundary in this paper we give an idea which does not require any pressure information on the boundary and we hope that our idea could be applied to other problems such as exterior domain problem

abstract lp estimates for the cauchy problem with applications to the navier stokes equations in exterior domains abstract we apply an abstract perturbation theorem to derive global in time lq estimates for the cauchy problem and lq ls estimates for the nonstationary stokes equations in exterior domains this will be applied to obtain various new global in time estimates for weak solutions of the navier stokes equations

on l3 stability of the navier stokes system in exterior domains abstract this paper studies the stability of a stationary solution of the navier stokes system with a constant velocity at infinity in an exterior domain more precisely this paper considers the stability of the navier stokes system governing the stationary solution which belongs to the weak l 3 space l 3 under the condition that the initial datum belongs to a solenoidal l 3 space we prove that if both the l 3 norm of the initial datum and the l 3 norm of the stationary solution are sufficiently small then the system admits a unique global in time strong l 3 solution satisfying both l 3 asymptotic stability and l asymptotic stability moreover we investigate l 3 r asymptotic stability of the global in time solution using l p l q type estimates for the oseen semigroup and applying an equivalent norm on the lorentz space are key ideas to establish both the existence of a unique global in time strong or mild solution of our system and the stability of our solution

on the slow motion of a self propelled rigid body in a viscous incompressible fluid abstract in this paper we study the stokes approximation of the self propelled motion of a rigid body in a viscous liquid that fills all the three dimensional space exterior to the body we prove the existence and uniqueness of strong solution to the coupled systems of equations describing the motion of the system body liquid for any time and any regular distribution of velocity on the boundary of the body for the corresponding stationary problem we derive l p estimates for the solution in terms of the data finally we prove that every steady solution is attainable as the limit when t of an unsteady self propelled solution which starts from rest

a numerical solution for the simultaneous disturbance decoupling and row by row decoupling problem the numerical computation of the simultaneous disturbance decoupling and row by row decoupling problem is considered based on a condensed form for the system matrices the solvability of the simultaneous disturbance decoupling and row by row decoupling problem is reduced to the verification of an integer equality and the nonsingularity of a lower dimensional constant matrix the condensed form we use is computed using only orthogonal transformations which can be implemented in a numerically stable way hence it leads directly to an effective numerical method for solving the disturbance decoupling and row by row decoupling problem using existing tools such as lapack and matlab our result complements existing geometric and structural approaches which are of a theoretical nature and are not suitable for numerical computation

boundary layer effects for the 2 d boussinesq equations with vanishing diffusivity limit in the half plane nsfc 40890150 10801111 10971171 national basic research program 2005cb321700 natural science foundation of fujian province of china 2010j05011 fundamental research funds for the central universities 2010121006

controllability for distributed bilinear systems this paper studies controllability of systems of the form dw dt mathcal a w p t mathcal b w where mathcal a is the infinitesimal generator of a c 0 semigroup of bounded linear operators e mathcal a t on a banach space x mathcal b x to x is a c 1 map and p in l 1 0 t mathbb r is a control the paper i gives conditions for elements of x to be accessible from a given initial state w 0 and ii shows that controllability to a full neighborhood in x of w 0 is impossible for dim x infty examples of hyperbolic partial differential equations are provided

small amplitude swimming of a sphere abstract we study small amplitude swimming of a deformable sphere in a viscous incompressible fluid we assue that the surface displacement varies harmonically in time and calculate the resulting swimming velocity in perturbation theory to second order in the diplacement the optimum efficiency of swimming may be evaluated from the maximum eigenvalue of a hermitian matrix we find the optimum efficiency for the class of swimming motions for which the first order flow velocity is irrotational a closed form expression is constructed for the corresponding surface displacement

a canonical form for the inclusion principle of dynamic systems the inclusion principle provides a mathematical framework for comparing behavior of dynamic systems having different dimensions our main objective is to derive a canonical form for larger systems expansions that are obtained by expanding smaller systems contractions the form offers full freedom in selecting appropriate matrices for the expansion contraction process we will broaden the form to include feedback and propose an explicit characterization of contractible control laws subject to overlapping information structure constraints

adaptive density estimation for directional data using needlets this paper is concerned with density estimation of directional data on the sphere we introduce a procedure based on thresholding on a new type of spherical wavelets called needlets we establish a minimax result and prove its optimality we are motivated by astrophysical applications in particular in connection with the analysis of ultra high energy cosmic rays

preservation of controllability observability in expanded systems the result contributed by the article is that controllability observability of an original continuous time lti dynamic system can always be simultaneously preserved in expanded systems within the inclusion principle when using block structured complementary matrices this new structure offers more degrees of freedom for the selection of specific complementary matrices than well known used cases such as aggregations and restrictions which enable such preservation only in certain special cases a complete unrestricted transmission of these qualitative properties from the original controllable observable system to its expansion is a basic requirement on the expansion contraction process mainly when controllers observers are designed in expanded systems to be consequently contracted for implementation in initially given systems an original system composed of two overlapped subsystems is adopted as a general prototype ease a numerical example is supplied

decentralized control and overlapping decomposition of mechanical systems part 1 system decomposition this paper improves a new inclusion concept called txtension to mechanical systems described by matrix second order equations recent work on specialization of the inclusion principle has been generalized to the expansion and contraction of input state and output spaces but without the possibility of constructing completely general contractible controllers in this paper necessary and sufficient conditions for extensions and contractible feedback controllers are proved they enable the construction of general contractible controllers without any constraint on the structure of controllers for mechanical systems

global existence of weak solutions to 3d navier stokes ibvp with non decaying initial data in exterior domains abstract we consider the navier stokes initial boundary value problem in 3d exterior domains with non decaying initial data we investigate the existence of weak solutions defined for all t 0 for large non decaying initial data to achieve the result we extend the half space technique developed by maremonti and shimizu 2018 26 to the case of an exterior domain

an existence theorem for the navier stokes flow in the exterior of a rotating obstacle we consider the three dimensional navier stokes initial value problem in the exterior of a rotating obstacle it is proved that a unique solution exists locally in time if the initial velocity possesses the regularity l 1 2 this regularity assumption is the same as that in the famous paper of fujita kato an essential step for the proof is the deduction of a certain smoothing property together with estimates near t 0 of the semigroup which is not an analytic one generated by the operator in the space l 2 where stands for the angular velocity of the rotating obstacle and p denotes the projection associated with the helmholtz decomposition

an initial and boundary value problem modeling of fish like swimming in this paper we consider an initial and boundary value problem that models the self propelled motion of solids in a bidimensional viscous incompressible fluid the self propelling mechanism consisting of appropriate deformations of the solids is a simplified model of the propulsion mechanism of fish like swimmers the governing equations consist of the navier stokes equations for the fluid coupled to newton s laws for the solids since we consider the case in which the fluid solid system fills a bounded domain we have to tackle a free boundary value problem the main theoretical result in the paper asserts the global existence and uniqueness up to possible contacts of strong solutions of this problem the second novel result of this work is the provision of a numerical method for the fluid solid system this method provides a simulation of the simultaneous displacement of several swimmers and is tested on several examples

existence of weak solutions for the motion of rigid bodies in a viscous fluid we study the evolution of a finite number of rigid bodies within a viscous incompressible fluid in a bounded domain of r d d 2 or 3 with dirichlet boundary conditions by introducing an appropriate weak formulation for the complete problem we prove existence of solutions for initial velocities in h 1 0 omega in the absence of collisions solutions exist for all time in dimension 2 whereas in dimension 3 the lifespan of solutions is infinite only for small enough data

the motion of a fluid rigid ball system at the zero limit of the rigid ball radius we study the limiting motion of a system of rigid ball moving in a navier stokes fluid in mathbb r 3 as the radius of the ball goes to zero recently dashti and robinson solved this problem in the two dimensional case in the absence of rotation of the ball dashti and robinson in arch rational mech anal 200 285 312 2011 this restriction was caused by the difficulty in obtaining appropriate uniform bounds on the second order derivatives of the fluid velocity when the rigid body can rotate in this paper we show how to obtain the required uniform bounds on the velocity fields in the three dimensional case these estimates then allow us to pass to the zero limit of the ball radius and show that the solution of the coupled system converges to the solution of the navier stokes equations describing the motion of only fluid in the whole space the trajectory of the centre of the ball converges to a fluid particle trajectory which justifies the use of rigid tracers for finding lagrangian paths of fluid flow

decentralized control using quasi block diagonal dominance of transfer function matrices the purpose of this paper is to present a generalization of the nyquist array method to blockwise decompositions which is based upon a new version of block diagonal dominance an additional flexibility of the proposed method is in partitioning of the system matrices into disjoint as well as overlapping submatrices which increases considerably the class of control systems which can be designed via block diagonal dominance within this framework the controllers for individual subsystems can be designed independently of each other so that their union represents a decentralized controller for the overall system