long time estimates in the mean field limit in this paper we prove a stability result for measure perturbations of some class of stationary distributions of a vlasov equation we use this result to prove that the n particles approximation of these stationary distributions is uniformly valid on a time scale of order n1 8 which is much longer than the usual log n scale we also prove similar results for the approximation of the two dimensional euler equation by the vortex blob method

a remark on regularity criterion for the 3d hall mhd equations based on the vorticity in this paper we investigate the regularity criterion for the local in time classical solution to the three dimensional 3d incompressible hall magnetohydrodynamic equations hall mhd it is proved that the control of the vorticity alone can ensure the smoothness of the solution

global existence and asymptotic behavior for the 3d generalized hall mhd system abstract in this paper we consider the global existence for the 3d generalized hall mhd equations with fractional dissipative terms u and b under small initial data in the setting of sobolev norms with lower regularity for the global existence we enlarge the range of dissipative exponents from 1 7 6 to 1 3 2 which established in a recent work in addition the long time behavior and rates of decay for both the solutions and higher derivatives in different sobolev spaces are obtained by using the fourier splitting method which extends the previous work by chae and schonbek

a local proof for the characterization of young measures generated by sequences in bv this work presents a new proof of the recent characterization theorem for generalized young measures generated by sequences in bv by kristensen and rindler 2010 14 the present argument is based on a localization technique together with a local hahn banach argument in novel function spaces combined with an application of alberti s rank one theorem this strategy avoids employing a relaxation theorem as in the previously known proof and the new tools introduced in its course should prove useful in other contexts as well in particular we introduce homogeneous young measures separately at regular and singular points which exhibit rather different behavior than the classical homogeneous young measures as an application we show how for bv young measures with an atomic part one can find a generating sequence respecting this structure

the small dispersion limit of the korteweg de vries equation iii in parts i and ii we have derived explicit formulas for the distribution limit u of the solution of the kdv equation as the coefficient of uxxx tends to zero this formula contains n parameters 1 n whose values as well as whose number depends on x and t in section 4 we have shown that for t tb n 1 and the value of was determined in section 5 we have shown that the parameters i satisfy a nonlinear system of partial differential equations in part iii section 6 we show that for t large n 3 and we determine the asymptotic behavior of 1 2 3 and of u and u2 for t large the explicit formulas show that u and u2 are o t 1 and o t 2 respectively see formulas 6 2 and 6 24 in section 7 we study initial data whose value tends to zero as x and to 1 as x if one accepts some plausible guesses about the behavior of solutions with such initial data we derive an explicit formula for the solution and determine the large scale asymptotic behavior of the solution the function s is expressible in terms of complete elliptic integrals a similar formula is derived for u2 in section 8 we indicate how to extend the treatment of this series of papers to multihumped but still negative initial data

analytic results related to magneto hydrodynamic turbulence abstract analytic results are provided for topics related to the magneto hydrodynamic turbulence scaling exponents of general structure functions geometric criteria for singularity formation and dissipative solutions

h measures a new approach for studying homogenisation oscillations and concentration effects in partial differential equations new mathematical objects called h measures are introduced for studying oscillations and concentration effects in partial differential equations applications to transport properties and to homogenisation are given as an example of the new results which can be obtained by this approach

on global existence energy decay and blow up criteria for the hall mhd system in this paper we obtain global existence and energy decay for 3d hall magnetohydrodynamics hall mhd system with u and b besides the classical energy method and besov space techniques the interpolating inequalities are crucial in the proof of decay estimates then two osgood type blow up criteria are established our results improve the corresponding theorems in 3 and 4 in addition we establish two beale kato majda blow up criterion for the generalized version of hall mhd with u and b 1

global positioning of robot manipulators via pd control plus a class of nonlinear integral actions deals with the position control of robot manipulators proposed is a simple class of robot regulators consisting of a linear proportional derivative pd feedback plus an integral action of a nonlinear function of position errors by using lyapunov s direct method and lasalle s invariance principle the authors characterize a class of such nonlinear functions and they provide explicit conditions on the regulator gains to ensure global asymptotic stability these regulators offer an attractive alternative to global regulation compared with the well known partially model based pd control with gravity compensation and pd control with desired gravity compensation

global wellposedness for hall mhd equations abstract this paper concerns the wellposedness problem of hall mhd system the mild solution of hall mhd equations exists globally in the nonhomogeneous lei lin space setting provided that the initial data satisfies u 0 x 1 x 0 b 0 x 1 x 0 min 2 4 where is the viscosity of the fluid and is the magnetic diffusion coefficient our global existence result covers rougher initial data and improves the previous results

quasiconvex elastodynamics weak strong uniqueness for measure valued solutions a weak strong uniqueness result is proved for measure valued solutions to the system of conservation laws arising in elastodynamics the main novelty brought forward by the present work is that the underlying stored energy function of the material is assumed strongly quasiconvex the proof employs tools from the calculus of variations to establish general convexity type bounds on quasiconvex functions and recasts them in order to adapt the relative entropy method to quasiconvex elastodynamics

a geometrical study of 3d incompressible euler flows with clebsch potentials a long lived euler flow and its power law energy spectrum abstract a simple initial condition for vorticity sin y z sin z x sin x y which has clebsch potentials has been identified to lead to a flow evolution with a very weak energy transfer this allows us to integrate the euler equations in time longer than commonly expected to reach a stage at which the total enstrophy attains its peak for the corresponding navier stokes flow it thereby enables us to study the relationship between the inviscid limit and totally inviscid behaviours numerically in spite of small energy dissipation rate the navier stokes flow shows a power law spectrum whose exponent is around 5 3 and 2 a similar behaviour is also observed for the euler flow in physical space this flow has groups of vorticity layers which hesitate to roll up

theory of convex local compactifications with applications to lebesgue spaces a general theory is developed to imbed continuously and densely a topological space with a boundedness into a compact possibly also locally compact and closed convex subset of a locally convex space a class of such convex compactifications of the lebesgue space l p ir n is then studied and particular cases are identified with some known ex tensions e g with young schonbek or diperna majda measures it enables a thorough investigation of their topological geometrical properties and relations between them affine continuous extensions of nemytskii mapping are systematically studied as well

global well posedness for navier stokes equations in critical fourier herz spaces abstract we prove the global well posedness for the 3d navier stokes equations in critical fourier herz spaces by making use of the fourier localization method and the littlewood paley theory the advantage of working in fourier herz spaces lies in that they are more adapted than classical besov spaces for estimating the bilinear paraproduct of two distributions with the summation of their regularity indexes exactly zero our result is an improvement of a recent theorem by lei and lin 2011 10

a regularity criterion for a generalized hall mhd system abstract this paper proves a regularity criterion for a 3d generalized hall mhd system in terms of velocity gradient in negative besov spaces

on the blow up criterion and small data global existence for the hall magnetohydrodynamics abstract in this paper we establish an optimal blow up criterion for classical solutions to the incompressible resistive hall magnetohydrodynamic equations we also prove two global in time existence results of the classical solutions for small initial data the smallness conditions of which are given by the suitable sobolev and the besov norms respectively although the sobolev space version is already an improvement of the corresponding result in 4 the optimality in terms of the scaling property is achieved via the besov space estimate the special property of the energy estimate in terms of b 2 1 s norm is essential for this result contrary to the usual mhd the global well posedness in the 2 1 2 dimensional hall mhd is wide open

convergence of the viscosity method for isentropic gas dynamics a convergence theorem for the method of artificial viscosity applied to the isentropic equations of gas dynamics is established convergence of a subsequence in the strong topology is proved without uniform estimates on the derivatives using the theory of compensated compactness and an analysis of progressing entropy waves

weak strong uniqueness for measure valued solutions to the ericksen leslie model equipped with the oseen frank free energy abstract we analyze the ericksen leslie system equipped with the oseen frank energy in three space dimensions recently the author introduced the concept of measure valued solutions to this system and showed the global existence of these generalized solutions in this paper we show that suitable measure valued solutions which fulfill an associated energy inequality enjoy the weak strong uniqueness property i e the measure valued solution agrees with a strong solution if the latter exists the weak strong uniqueness is shown by a relative energy inequality for the associated nonconvex energy functional

on the temporal decay for the hall magnetohydrodynamic equations abstract we establish temporal decay estimates for weak solutions to the hall magnetohydrodynamic equations with these estimates in hand we obtain algebraic time decay for higher order sobolev norms of small initial data solutions

oscillations and concentrations in weak solutions of the incompressible fluid equations the authors introduce a new concept of measure valued solution for the 3 d incompressible euler equations in order to incorporate the complex phenomena present in limits of approximate solutions of these equations one application of the concepts developed here is the following important result a sequence of leray hopf weak solutions of the navier stokes equations converges in the high reynolds number limit to a measure valued solution of 3 d euler defined for all positive times the authors present several explicit examples of solution sequences for 3 d incompressible euler with uniformly bounded local kinetic energy which exhibit complex phenomena involving both persistence of oscillations and development of concentrations an extensions of the concept of young measure is developed to incorporate these complex phenomena in the measure valued solutions constructed here

on the lagrangian and eulerian analyticity for the euler equations abstract we address preservation of the lagrangian analyticity radius of solutions to the euler equations belonging to natural analytic space based on the size of taylor or gevrey coefficients we prove that if the solution belongs to such space then the solution also belongs to it for a positive amount of time we also prove the local analog of this result for a sufficiently large gevrey parameter however we show that the preservation holds independently of the size of the radius finally we construct a solution which shows that the first result does not hold in the eulerian setting

regularity criterion for the 3d hall magneto hydrodynamics abstract this paper studies the regularity problem for the 3d incompressible resistive viscous hall magneto hydrodynamic hall mhd system the kolmogorov 41 phenomenological theory of turbulence 14 predicts that there exists a critical wavenumber above which the high frequency part is dominated by the dissipation term in the fluid equation inspired by this idea we apply an approach of splitting the wavenumber combined with an estimate of the energy flux to obtain a new regularity criterion the regularity condition presented here is weaker than conditions in the existing criteria prodi serrin type criteria for the 3d hall mhd system

a generalised pid type control scheme with simple tuning for the global regulation of robot manipulators with constrained inputs in this paper a globally stabilising pid type control scheme with a generalised saturating structure for robot manipulators under input constraints is proposed it gives rise to various families of bounded pid type controllers whose implementation is released from the exact knowledge of the system parameters and model structure compared to previous approaches of the kind the proposed scheme is not only characterised by its generalised structure but also by its very simple tuning criterion the simplest hitherto obtained in the considered analytical framework experimental results on a 3 degree of freedom direct drive manipulator corroborate the efficiency of the proposed approach

the generation of modulated wavetrains in the solution of the korteweg de vries equation on demontre une relation entre la methode des ondes modulees de whitham et la methode de lax et levermore contenant la limite de petite dispersion

the small dispersion limit of the korteweg de vries equation ii in part i the scattering transform method is used to study the weak limit of solutions to the initial value problem for the korteweg devries kdv equation as the dispersion tends to zero in that limit the associated schrodinger operator becomes semiclassical so the exact scattering data is replaced by its corresponding wkb expressions only nonpositive initial data are considered in that case the limiting reflection coefficient vanishes the explicit solution of kay and moses for the reflectionless inverse transform is then analyzed and the weak limit valid for all time is characterized by a quadratic minimum problem with constraints this minimum problem is reduced to a riemann hilbert problem in function theory in parts ii and iii we use function theoretical methods to solve the riemann hilbert problem in terms of solutions to an auxiliary initial value problem the weak limit satisfies the kdv equation with the dispersive term dropped until its derivatives become infinite up to that time the weak limit is a strong l2 limit at later times the weak limit is locally described by whitham s averaged equations or more generally by the equations found by flaschka et al using multiphase averaging for large times behavior of the weak limit is studied directly from the minimum problem

a criterion for the equivalence of the birkhoff rott and euler descriptions of vortex sheet evolution in this article we consider the evolution of vortex sheets in the plane both as a weak solution of the two dimensional incompressible euler equations and as a weak solution of the birkhoff rott equations we begin by discussing the classical birkhoff rott equations with respect to arbitrary parametrizations of the sheet we introduce a notion of weak solution to the birkhoff rott system and we prove consistency of this notion with the classical formulation of the equations our main purpose in this paper is to present a sharp criterion for the equivalence of the weak euler and weak birkhoff rott descriptions of vortex sheet dynamics

global well posedness and ill posedness for the navier stokes equations with the coriolis force in function spaces of besov type abstract we consider the initial value problems for the navier stokes equations in the rotational framework we introduce function spaces b p q s r 3 of besov type and prove the global in time existence and the uniqueness of the mild solution for small initial data in our space b 1 2 1 r 3 near bmo 1 r 3 furthermore we also discuss the ill posedness for the navier stokes equations with the coriolis force which implies the optimality of our function space b 1 2 1 r 3 for the global well posedness

a remark on the blow up criterion for the 3d hall mhd system in besov spaces abstract in this paper we consider the three dimensional hall magnetohydrodynamic system and show that if the velocity and the magnetic fields belong to some critical besov spaces on 0 t then the solution can be extended smoothly beyond t this improves previous results

self similar 2d euler solutions with mixed sign vorticity we construct a class of self similar 2d incompressible euler solutions that have initial vorticity of mixed sign the boundaries between regions of positive and negative vorticity form algebraic spirals similar to the kaden spiral and as opposed to prandtl s logarithmic vortex spirals also unlike the prandtl case spirals are not initially present

a multi fluid compressible system as the limit of weak solutions of the isentropic compressible navier stokes equations this paper mainly concerns the mathematical justification of a viscous compressible multi fluid model linked to the baer nunziato model used by engineers see for instance ishii thermo fluid dynamic theory of two phase flow eyrolles paris 1975 under a stratification assumption more precisely we show that some approximate finite energy weak solutions of the isentropic compressible navier stokes equations converge on a short time interval to the strong solution of this viscous compressible multi fluid model provided the initial density sequence is uniformly bounded with corresponding young measures which are linear convex combinations of m dirac measures to the authors knowledge this provides in the multidimensional in space case a first positive answer to an open question see hillairet j math fluid mech 9 343 376 2007 with a stratification assumption the proof is based on the weak solutions constructed by desjardins commun partial differ equ 22 5 6 977 1008 1997 and on the existence and uniqueness of a local strong solution for the multi fluid model established by hillairet assuming initial density to be far from vacuum in a first step adapting the ideas from hoff and santos arch ration mech anal 188 509 543 2008 we prove that the sequence of weak solutions built by desjardins has extra regularity linked to the divergence of the velocity without any relation assumption between and coupled with the uniform bound of the density property this allows us to use appropriate defect measures and their nice properties introduced and proved by hillairet aspects interactifs de la m ecanique des fluides phd thesis ens lyon 2005 in order to prove that the young measure associated to the weak limit is the convex combination of m dirac measures finally under a non degeneracy assumption of this combination stratification assumption this provides a multi fluid system using a weak strong uniqueness argument we prove that this convex combination is the one corresponding to the strong solution of the multi fluid model built by hillairet if initial data are equal we will briefly discuss this assumption to complete the paper we also present a blow up criterion for this multi fluid system following huang et al in serrin type criterion for the three dimensional viscous compressible flows arxiv 2010

regularity criteria and small data global existence to the generalized viscous hall magnetohydrodynamics in this paper we establish the regularity criteria of solutions to the three space dimensions generalized viscous hall magnetohydrodynamics moreover we also prove that there exist classical solutions globally in time to the generalized viscous hall mhd if the initial data is small enough or the fractional laplacian dissipation powers and are suitably large these results are some improvements of very recent work chae and lee 2014 established by chae and lee

a special class of stationary flows for two dimensional euler equations a statistical mechanics description we consider the canonical gibbs measure associated to an vortex system in a bounded domain at inverse temperature widetilde beta and prove that in the limitn widetilde beta n n 1 where 8 here denotes the vorticity intensity of each vortex the one particle distribution function n nx x converges to a superposition of solutions of the following mean field equation left begin array 20 c varrho beta x frac e beta psi mathop smallint limits lambda e beta psi delta psi varrho beta in lambda psi partial lambda 0 end array right

the stability of feedback control with nonlinear saturating actuator time domain approach sufficient conditions for stability of closed loop systems with a saturating actuator are derived from the viewpoint of time domain the bellman gronwall inequality is used to investigate the stability of these systems three kinds of controllers are considered to treat this constrained control problem finally an example is given to illustrate the results

existence of global weak solutions to one component vlasov poisson and fokker planck poisson systems in one space dimension with measures as initial data we consider cauchy problems for the 1 d one component vlasov poisson and fokker planck poisson equations with the initial electron density being in the natural space of arbitrary non negative finite measures in particular the initial density can be a dirac measure concentrated on a curve which we refer to as electron sheet initial data these problems resemble both structurally and functional analytically cauchy problems for the 2 d euler and navier stokes equations in vorticity formulation with vortex sheet initial data here we need to define weak solutions more specifically than usual since the product of a finite measure with a function of bounded variation is involved we give a natural definition of the product establish its weak stability and existence of weak solutions follows our concept of weak solutions through the newly defined product is justified since solutions to the fokker planck poisson equation the analogue of navier stokes equation are shown to converge to weak solutions of the vlasov poisson equation as the fokker planck term vanishes the main difficulty is the aforementioned weak stability which we establish through a careful analysis of the explicit structure of these equations this is needed because the problem studied here is beyond the range of applicability of the velocity averaging compactness methods of diperna lions 1994 john wiley sons inc

reduced hausdorff dimension and concentration cancellation for two dimensional incompressible flow where v t v1 v2 is the fluid velocity p is the scalar pressure dv dt av at v v v and vo is an initial incompressible velocity field i e div vo 0 in this paper we study the detailed limiting behavior of approximate solution sequences for 2 d euler with vortex sheet initial data a sequence of smooth velocity fields v8 x t is an approximate solution sequence for 2 d euler provided that v is incompressible i e div v 0 and satisfies the following properties 1 the velocity fields v6 have uniformly bounded local kinetic energy i e

the zero dispersion limit of the korteweg de vries equation for initial potentials with non trivial reflection coefficient the inverse scattering method is used to determine the distribution limit as 0 of the solution u x t of the initial value problem ut 6uux 2uxxx 0 u x 0 v x where v x is a positive bump which decays sufficiently fast as x x the case v x 0 has been solved by peter d lax and c david levermore 8 9 10 the computation of the distribution limit of u x t as 0 is reduced to a quadratic maximization problem which is then solved

hydrodynamics in two dimensions and vortex theory we consider the navier stokes equation for a viscous and incompressible fluid inr2 we show that such an equation may be interpreted as a mean field equation vlasov like limit for a system of particles called vortices interacting via a logarithmic potential on which in addition a stochastic perturbation is acting more precisely we prove that the solutions of the navier stokes equation may be approximated in a suitable way by finite dimensional diffusion processes with the diffusion constant related to the viscosity as a particular case when the diffusion constant is zero the finite dimensional theory reduces to the usual deterministic vortex theory and the limiting equation reduces to the euler equation

functional and measure valued solutions of the euler equations for flows of incompressible fluids we consider the notion of a functional solution of the euler equations for incompressible fluid flows we show that a functional solution can be constructed under very weak a priori estimates on approximate solution sequences of the equation an estimate uniform in lloc1 together with weak consistency with the equation is sufficient to construct a solution we prove that if we have an estimate uniform in lloc2 available for the approximate solution sequence then the structured functional solution just described becomes a measure valued solution in the sense of diperna majda we also show that a functional solution can be obtained from a measure valued solution we give an example showing that a much higher concentration of energy than in the case of measure valued solutions is allowed by the approximation procedure of a functional solution

some geometric properties of the set of generalized young functionals this paper studies geometric properties in particular extreme points and rays of various generalizations of young measures applications of the knowledge of extreme points are illustrated on existence results for optimal control problems and on various convergence results for young measures by using the choquet theory

on a weak solution for a transonic flow problem on essaie d etablir l existence de solutions faibles pour un ecoulement stationnaire bidimensionnel irrotationnel compressible non visqueux dans un canal de longueur infinie ou autour d un profil aerodynamique la vitesse de l ecoulement etant donnee a l infini

ordinary differential equations transport theory and sobolev spaces we obtain some new existence uniqueness and stability results for ordinary differential equations with coefficients in sobolev spaces these results are deduced from corresponding results on linear transport equations which are analyzed by the method of renormalized solutions

development of multivariable pid controller gains in presence of measurement noise abstractthis paper examines the ability of a multivariable pid controller rejecting measurement noise without the use of any external filter the work first provides a framework for the design of the pid gains comprising of necessary and sufficient conditions for boundedness of trajectories and zero error convergence in presence of measurement noise it turns out that such convergence requires time varying gains subsequently novel recursive algorithms providing optimal and sub optimal time varying pid gains are proposed for discrete time varying linear multiple input multiple output mimo systems the development of the proposed optimal algorithm is based on minimising a stochastic performance index in presence of erroneous initial conditions white measurement noise and white process noise the proposed algorithms are shown to reject measurement noise provided that the system is asymptotically stable and the product of the input output coupling matrices is full column rank in addition convergence r

homogenization and convergence of the vortex method for 2 d euler equations with oscillatory vorticity fields the 2 d incompressible euler equations with oscillatory vorticity fields are studied a homogenization result for 2 d euler equations in velocity vorticity formulation is obtained and weak continuity of the equations is proved convergence of the vortex method is analyzed in the case when the continuous vorticity is not well resolved by the computational particles numerical results are given comparisons are made with the corresponding finite difference approximation

convergence of particle methods with random rezoning for the two dimensional euler and navier stokes equations we prove the convergence of a vortex method for the two dimensional euler and navier stokes equations when only weak solutions are available the approximation uses random rezoning at each time step and the convergence is obtained provided the various discretization parameters are linked by some power laws the techniques rely on compactness properties similar to those giving the existence of weak solutions

measure valued solutions and the phenomenon of blow down in logarithmic diffusion abstract the existence of solutions of elliptic and parabolic equations with data a measure has always been quite important for the general theory a prominent example being the fundamental solutions of the linear theory in nonlinear equations the existence of such solutions may find special obstacles that can be either essential or otherwise they may lead to more general concepts of solution we give a particular review of results in the field of nonlinear diffusion as a new contribution we study in detail the case of logarithmic diffusion associated with ricci flow in the plane where we can prove existence of measure valued solutions the surprising thing is that these solutions become classical after a finite time in that general setting the standard concept of weak solution is not adequate but we can solve the initial value problem for the logarithmic diffusion equation in the plane with bounded nonnegative measures as initial data in a suitable class of measure solutions we prove that the problem is well posed the phenomenon of blow down in finite time is precisely described initial point masses diffuse into the medium and eventually disappear after a finite time t i m i 4

beale kato madja type criteria of smooth solutions to 3d hall mhd flows in this article we study the initial value problem for the impressible hall mhd flows in three space dimensions several beale kato madja type blow up criteria of smooth solutions in term of the vorticity in homogeneous besov space are established

global mild solutions of navier stokes equations we establish a global well posedness of mild solutions to the three dimensional incompressible navier stokes equations if the initial data are in the space x 1 defined by x 1 f e d r 3 3 1 f d and if the norms of the initial data in x 1 are bounded exactly by the viscosity coefficient

optimal control problems with oscillations concentrations and discontinuities optimal control problems with oscillations chattering controls and concentrations impulsive controls can have integral performance criteria such that concentration of the control signal occurs at a discontinuity of the state signal techniques from functional analysis anisotropic parametrized measures are applied to give a precise meaning of the integral cost and to allow for the sound application of numerical methods we show how this can be combined with the lasserre hierarchy of semidefinite programming relaxations

an optimal stochastic multivariable pid controller a direct output tracking approach abstractthis paper deals with the design of an optimal stochastic controller possessing tracking capability of any reference output trajectory in the presence of measurement noise we consider multi input multi output linear time invariant systems and a proportional integral derivative pid controller the system under consideration needs not be stable a recursive algorithm providing optimal time varying pid gains is proposed for the case where the number of inputs is larger than or equal to the number of outputs the development of the proposed algorithm aims for per time sample minimisation of the mean square output error in the presence of erroneous initial conditions measurement noise and process noise necessary and sufficient conditions are provided for the convergence of the output error covariance in addition convergence results are presented for discretised continuous time plants simulation results are included to illustrate the performance capabilities of the proposed algorithm performan

young measures generated by ideal incompressible fluid flows in their seminal paper diperna and majda commun math phys 108 4 667 689 1987 introduced the notion of a measure valued solution for the incompressible euler equations in order to capture complex phenomena present in limits of approximate solutions such as persistence of oscillation and development of concentrations furthermore they gave several explicit examples exhibiting such phenomena in this paper we show that any measure valued solution can be generated by a sequence of exact weak solutions in particular this gives rise to a very large arguably too large set of weak solutions of the incompressible euler equations

characterization of generalized gradient young measures generated by sequences in w1 1 and bv generalized young measures as introduced by diperna and majda commun math phys 108 667 689 1987 provide a quantitative tool for studying the one point statistics of oscillation and concentration in sequences of functions in this work after developing a functional analytic framework for such measures including a compactness theorem and results on the generation of such young measures by l1 bounded sequences or even by sequences of bounded radon measures we turn to investigation of those young measures that are generated by bounded sequences of w1 1 gradients or bv derivatives we provide several techniques to manipulate such measures including shifting averaging and approximation by piecewise homogeneous young measures and then establish the main new result of this work the duality characterization of the set of bv or w1 1 gradient young measures in terms of jensen type inequalities for quasiconvex functions with linear growth at infinity this result is the natural generalization of the kinderlehrer pedregal theorem arch ration mech anal 115 329 365 1991 j geom anal 4 59 90 1994 for classical young measures to the w1 1 and bv case and contains its version for weakly converging sequences in w1 1 as a special case finally we give an application to a new lower semicontinuity theorem in bv

lagrangian solutions to the 2d euler system with l1 vorticity and infinite energy we consider solutions to the two dimensional incompressible euler system with only integrable vorticity thus with possibly locally infinite energy with such regularity we use the recently developed theory of lagrangian flows associated to vector fields with gradient given by a singular integral in order to define lagrangian solutions for which the vorticity is transported by the flow we prove strong stability of these solutions via strong convergence of the flow under the only assumption of l1 weak convergence of the initial vorticity the existence of lagrangian solutions to the euler system follows for arbitrary l1 vorticity relations with previously known notions of solutions are established

generalised solutions for fully nonlinear pde systems and existence uniqueness theorems we introduce a new theory of generalised solutions which applies to fully nonlinear pde systems of any order and allows for merely measurable maps as solutions this approach bypasses the standard problems arising by the application of distributions to pdes and is not based on either integration by parts or on the maximum principle instead our starting point builds on the probabilistic representation of derivatives via limits of difference quotients in the young measures over a toric compactification of the space of jets after developing some basic theory as a first application we consider the dirichlet problem and we prove existence uniqueness partial regularity of solutions to fully nonlinear degenerate elliptic 2nd order systems and also existence of solutions to the laplace system of vectorial calculus of variations in l

on diperna majda concentration sets for two dimensional incompressible flow abstract the existence of weak solutions to the incompressible euler equations for vortex sheet initial data is an open problem two approaches to this problem are the smoothing of vortex sheets by approximated identifies which provides a sequence of smooth initial conditions converging to vortex sheet initial conditions for which classical solutions exist and viscous smoothing of vortex sheets these ideas are among the principal motivations for the recent series of papers in which the nature of the limiting behavior of sequences of solutions of euler s equations are examined the concept of generalized young measure valued solution of the euler equations is introduced in two dimensions approximate solution sequences always have subsequences which converge in an appropriate sense to non oscillatory generalized young measure valued solutions of euler s equations infinitesimal vortices of zero circulation were described in and named phantom vortices the vortices in our example are somewhat different in that they have two length scales the two length scales are important for one cannot pack phantom vortices on successively finer lattices as above keeping the vorticity absolutely summable without at the same time obtaining strong convergence in l sq reprints

counter examples to concentration cancellation we study the existence and the asymptotic behavior of large amplitude high frequency oscillating waves subjected to the two dimensional burger equation this program is achieved by developing tools related to supercritical wkb analysis by selecting solutions which are divergence free we show that incompressible or compressible two dimensional euler equations are not locally closed for the weak l2 topology

a remark on vorticity maximal function in this note the following inequality is proved for any nonnegative measure h 1 r2 x r2 and 0 r 1 there holds 1 b x r c ln1r 12 h 1 where c is a positive constant using 1 an estimate for the vorticity maximal function similar to the estimate in majda a majda remarks on weak solutions for vortex sheets with a distinguished sign indiana univ math j 42 1993 921 939 is established without assuming the initial vorticity having compact support from this a more simple proof of the delort s celebrated theorem j m delort existence de mappes de fourbillon en dimension deux j amer math soc 4 1991 553 586 is presented

regularity criteria for the incompressible hall magnetohydrodynamic equations abstract we establish some new regularity criteria for the three dimensional incompressible hall magnetohydrodynamic equations

further advancements on the output feedback global continuous control for the finite time and exponential stabilisation of bounded input mechanical systems desired conservative force compensation and experiments global saturating proportional saturating derivative sp sd type continuous control for the finite time or local exponential stabilisation of mechanical systems with bounded inputs is achieved a

convergence of a galerkin method for 2 d discontinuous euler flows we prove the convergence of a discontinuous galerkin method approximating the 2 d incompressible euler equations with discontinuous initial vorticity 0 2 l 2 furthermore when 0 2 l the whole sequence is shown to be strongly convergent this is the first convergence result in numerical approximations of this general class of discontinuous flows some important flows such as vortex patches belong to this class c 2000 john wiley sons inc

ill posedness for the navier stokes equations in critical besov spaces b q 1 abstract we study the cauchy problem for the incompressible navier stokes equations in two and higher spatial dimensions 0 1 u t u u u p 0 div u 0 u 0 x u 0 for arbitrarily small 0 we show that the solution map u 0 u in critical besov spaces b q 1 q 1 2 is discontinuous at origin it is known that the navier stokes equation is globally well posed for small data in bmo 1 20 taking notice of the embedding b q 1 bmo 1 q 2 we see that for sufficiently small 0 u 0 b q 1 q 2 can guarantee that 0 1 has a unique global solution in bmo 1 however this solution is instable in b q 1 and the solution can have an inflation in b q 1 for certain initial data

a stochastic pid controller for a class of mimo systems abstractthis paper deals with the design of a controller possessing tracking capability of any realisable reference trajectory while rejecting measurement noise we consider discrete time varying multi input multi output stable linear systems and a proportional integral derivative pid controller a novel recursive algorithm estimating the time varying pid gains is proposed the development of the proposed algorithm is based on minimising a stochastic performance index the implementation of the proposed algorithm is described and boundedness of trajectories and convergence characteristics are presented for a discretised continuous time model simulation results are included to illustrate the performance capabilities of the proposed algorithm

statistical solutions and onsager s conjecture abstract we prove a version of onsager s conjecture on the conservation of energy for the incompressible euler equations in the context of statistical solutions as introduced recently by fjordholm et al 2017 as a byproduct we also obtain an alternative proof for the conservative direction of onsager s conjecture for weak solutions under a weaker besov type regularity assumption than previously known

on global output feedback regulation of euler lagrange systems with bounded inputs we identify a class of euler lagrange systems with bounded inputs that can be globally asymptotically stabilized via dynamic output feedback in particular we prove that if the system is fully actuated and the forces due to the potential field can be dominated by the constrained control signals then global output feedback regulation is still possible incorporating some suitable saturation functions in the controller

a new regularity criterion for the 3d generalized hall mhd system with β 12 1 abstract in this paper we consider the generalized hall mhd system in dimension three a new regularity criterion is established for 1 2 1

brief semiglobal stability of saturated linear pid control for robot manipulators this paper addresses the position regulation problem of robot manipulators under control input constraints it is proven that the robot system under a saturated linear pid control is semiglobally asymptotically stable if the torque bounds are larger than gravitational torques and if the proportional gain is large enough and the integral gain is small enough the stability analysis makes use of singular perturbation tools and the results are illustrated via numerical simulations

relative entropy for hyperbolic parabolic systems and application to the constitutive theory of thermoviscoelasticity we extend the relative entropy identity to the class of hyperbolic parabolic systems whose hyperbolic part is symmetrizable the resulting identity in the general theory is useful for providing stability of viscous solutions and yields a convergence result in the zero viscosity limit to smooth solutions in an l p framework it also provides a weak strong uniqueness theorem for measure valued solutions of the hyperbolic problem in the second part the relative entropy identity is developed for the systems of gas dynamics for viscous and heat conducting gases and for the system of thermoviscoelasticity both including viscosity and heat conduction effects the dissipation mechanisms and the concentration measures play different roles when applying the method to the general class of hyperbolic parabolic systems and to the specific examples and their ramifications are highlighted

vanishing viscosity limit for homogeneous axisymmetric no swirl solutions of stationary navier stokes equations abstract 1 homogeneous axisymmetric no swirl solutions of three dimensional incompressible stationary navier stokes equations which are smooth on the unit sphere minus the north and south poles have been classified in this paper we study the vanishing viscosity limit of sequences of these solutions as the viscosity tends to zero some sequences of solutions c l o c m converge to solutions of euler equations on the sphere minus the poles while for other sequences of solutions transition layer behaviors occur for every latitude circle there are sequences which c l o c m converge respectively to different solutions of the euler equations on the spherical caps above and below the latitude circle we give detailed analysis of these convergence and transition layer behaviors

local ill posedness of the incompressible euler equations in c 1 and b 1_ infty 1 we show that the 2d euler equations are not locally well posed in the sense of hadamard in the c 1 space and in the besov space b 1 infty 1 our approach relies on the technique of lagrangian deformations of bourgain and li strong ill posedness of the incompressible euler equations in borderline sobolev spaces arxiv 1307 7090 we show that the assumption that the data to solution map is continuous in either c 1 or b 1 infty 1 leads to a contradiction with a result in w 1 p of kato and ponce rev mat iberoam 2 73 88 1986