the segal bargmann coherent state transform for compact lie groups abstract let k be an arbitrary compact connected lie group we describe on k an analog of the segal bargmann coherent state transform and we prove theorem 1 that this generalized coherent state transform maps l 2 k isometrically onto the space of holomorphic functions in l 2 g where g is the complexification of k and where is an appropriate heat kernel measure on g the generalized coherent state transform is defined in terms of the heat kernel on the compact group k and its analytic continuation to the complex group g we also define a k averaged version of the coherent state transform and we prove a similar result for it theorem 2 in the appendix we describe the coherent states which motivate the definitions of these transforms in section 9 we obtain inversion formulas for both the coherent state transform and the k averaged coherent state transform theorems 3 4 as a consequence we obtain formulas for certain bergman kernels on the complex group g theorems 5 6 in section 10 we derive a general paley wiener theorem for k and we exhibit a family of convolution transforms each of which is an isometric isomorphism of l 2 k onto a certain l 2 space of holomorphic functions on g these transforms include the k averaged coherent state transform as a special case we also discuss the analogous results for r 1 the results of section 10 are theorems 7 10 finally in section 11 we discuss the case of quotient spaces we prove theorem 11 that both the coherent state transform and the k averaged coherent state transform pass in a natural way from k to k h where h is a closed connected subgroup of k

a new bernstein s inequality and the 2d dissipative quasi geostrophic equation we show a new bernstein s inequality which generalizes the results of cannone planchon danchin and lemarie rieusset as an application of this inequality we prove the global well posedness of the 2d quasi geostrophic equation with the critical and super critical dissipation for the small initial data in the critical besov space and local well posedness for the large initial data

the segal bargmann transform for the heat equation associated with root systems we study the heat equation associated to a multiplicity function on a root system where the corresponding laplace operator has been defined by heckman and opdam in particular we describe the image of the associated segal bargmann transform as a space of holomorphic functions in the case where the multiplicity function corresponds to a riemannian symmetric space g k of non compact type we obtain a description of the image of the space of k invariant l2 function on g k under the segal bargmann transform associated to the heat equation on g k thus generalizing and reproving a result of b hall and j mitchell for spaces of complex type

global well posedness issues for the inviscid boussinesq system with yudovich s type data the present paper is dedicated to the study of the global existence for the inviscid two dimensional boussinesq system we focus on finite energy data with bounded vorticity and we find out that under quite a natural additional assumption on the initial temperature there exists a global unique solution no smallness conditions are imposed on the data the global existence issues for infinite energy initial velocity and for the benard system are also discussed

segal bargmann transforms associated with finite coxeter groups using a polarization of a suitable restriction map and heat kernel analysis we construct a generalized segal bargmann transform associated with every finite coxeter group g on n we find the integral representation of this transform and we prove its unitarity to define the segal bargmann transform we introduce a hilbert space open image in new window of holomorphic functions on open image in new window with reproducing kernel equal to the dunkl kernel the definition and properties of open image in new window extend naturally those of the well known classical fock space the generalized segal bargmann transform allows to exhibit some relationships between the dunkl theory in the schrodinger model and in the fock model further we prove a branching decomposition of open image in new window as a unitary open image in new window module and a general version of hecke s formula for the dunkl transform

global regularity results for the 2d boussinesq equations and micropolar equations with partial dissipation abstract this paper establishes the global regularity of the two dimensional 2d boussinesq equations and micropolar equations with partial dissipation our first result is the global regularity of the 2d boussinesq equations with fractional vertical dissipation in the horizontal velocity horizontal dissipation in the vertical velocity and zero thermal diffusion which is shown by taking advantage of the nice structure of the 2d boussinesq equations and several refined commutator estimates the second goal of this paper is to consider a system of the 2d incompressible micropolar equations with vertical dissipation in the horizontal velocity equation horizontal dissipation in the vertical velocity equation and the fractional dissipation in the micro rotation velocity in order to overcome the difficulty caused by the lack of full laplacian diffusion in the velocity equations we fully exploit the nice structure of the corresponding equations to show that this equations with arbitrarily small 0 always possesses a unique global classical solution

on the value of information in system identification bounded noise case assuming instantaneous bounds on the noise system parameter identification is formulated as membership set estimation problem sequential algorithms are constructed to estimate the membership sets of the parameters which are consistent with the measurements and the noise constraints the important new feature of the proposed algorithms is their ability to ignore redundant data the efficient data extraction property of the new algorithms is achieved with small computational effort and with improved performance when compared to the least square algorithm the convergence properties and the notion of identifiability in the set theoretic context are also studied

linear systems with state and control constraints the theory and application of maximal output admissible sets the initial state of an unforced linear system is output admissible with respect to a constraint set y if the resulting output function satisfies the pointwise in time condition y t in y t or 0 the set of all possible such initial conditions is the maximal output admissible set o sub infinity the properties of o sub infinity and its characterization are investigated in the discrete time case it is generally possible to represent o sub infinity or a close approximation of it by a finite number of functional inequalities practical algorithms for generating the functions are described in the continuous time case simple representations of the maximal output admissible set are not available however it is shown that the discrete time results may be used to obtain approximate representations

global regularity of 2d leray alpha regularized incompressible magneto micropolar equations abstract in this paper we consider a cauchy problem of the 2d leray regularized incompressible magneto micropolar equations the global smooth solution of the cauchy problem for the equations with zero angular viscosity and zero magnetic diffusion or with only angular viscosity and magnetic diffusion are established

global regularity results for the 2d boussinesq equations with vertical dissipation abstract the two dimensional 2d incompressible boussinesq equations model geophysical fluids and play an important role in the study of the raleigh bernard convection mathematically this 2d system retains some key features of the 3d navier stokes and euler equations such as the vortex stretching mechanism the issue of whether the 2d boussinesq equations always possess global in time classical solutions can be difficult when there is only partial dissipation or no dissipation at all this paper obtains the global regularity for two partial dissipation cases and proves several global a priori bounds for two other prominent partial dissipation cases these results take us one step closer to a complete resolution of the global regularity issue for all the partial dissipation cases involving the 2d boussinesq equations

global existence of three dimensional incompressible magneto micropolar system with mixed partial dissipation magnetic diffusion and angular viscosity abstract the magneto micropolar fluid flows describe the motion of electrically conducting micropolar fluids in the presence of a magnetic field the issue of whether the strong solution of magneto micropolar equations in three dimensional can exist globally in time with large initial data is still unknown in this paper we deal with the cauchy problem of the three dimensional magneto micropolar system with mixed partial dissipation magnetic diffusion and angular viscosity more precisely the global existence of smooth solutions to the three dimensional incompressible magneto micropolar fluid equations with mixed partial dissipation magnetic diffusion and angular viscosity are obtained by energy method under the assumption that h 1 norm of the initial data u 0 b 0 w 0 sufficiently small namely u 0 b 0 0 h 1 r 3 2 e 2 where e is a sufficiently small positive number this work follows the techniques in the paper of cao and wu 2011

global regularity for 2d magneto micropolar equations with only micro rotational velocity dissipation and magnetic diffusion abstract this paper studies the global regularity of classical solutions to 2d magneto micropolar fluid equations with only micro rotational velocity dissipation and magnetic diffusion here the micro rotational velocity dissipation and magnetic diffusion are given by and b making use of several combined quantities maximal regularity of heat operator and littlewood paley decomposition theory we establish a regularity criterion in terms of magnetic field for the case 1 and the global regularity for 1 the regularity criterion given here is also new even for the 2d magnetohydrodynamic equations in addition to prove these two main results as preparation we establish a new global a priori estimate for magnetic field namely b l 0 t l p r 2 with p 2 which also holds for the 2d magnetohydrodynamic equations as a particular case

global well posedness of the 2d boussinesq equations with vertical dissipation we prove the global well posedness of the two dimensional boussinesq equations with only vertical dissipation the initial data u 0 theta 0 are required to be only in the space x f in l 2 mathbb r 2 partial x f in l 2 mathbb r 2 and thus our result generalizes that of cao and wu arch rational mech anal 208 985 1004 2013 where the initial data are assumed to be in h 2 mathbb r 2 the assumption on the initial data is at the minimal level that is required to guarantee the uniqueness of the solutions a logarithmic type limiting sobolev embedding inequality for the l infty mathbb r 2 norm in terms of anisotropic sobolev norms and a logarithmic type gronwall inequality are established to obtain the global in time a priori estimates which guarantee the local solution to be a global one

limiting case of the sobolev inequality in bmo with application to the euler equations we shall prove a logarithmic sobolev inequality by means of the bmo norm in the critical exponents as an application we shall establish a blow up criterion of solutions to the euler equations

technical communique a line search improvement of efficient mpc a recent efficient model predictive control mpc strategy uses a univariate newton raphson procedure to solve a dual problem but is not amenable to warm starting or early termination by solving a primal problem the current note proposes a strategy which is more efficient than the newton raphson method and which enables warm starting and early termination performance improvements are demonstrated over the newton raphson method and alternative approaches based on quadratic programming or semidefinite programming

global regularity for the two dimensional anisotropic boussinesq equations with vertical dissipation this paper establishes the global in time existence of classical solutions to the two dimensional anisotropic boussinesq equations with vertical dissipation when only vertical dissipation is present there is no direct control on the horizontal derivatives and the global regularity problem is very challenging to solve this problem we bound the derivatives in terms of the l infty norm of the vertical velocity v and prove that v l r with 2 leqq r infty does not grow faster than sqrt r log r at any time as r increases a delicate interpolation inequality connecting v l infty and v l r then yields the desired global regularity

on segal bargmann analysis for finite coxeter groups and its heat kernel we prove identities involving the integral kernels of three versions two being introduced here of the segal bargmann transform associated to a finite coxeter group acting on a finite dimensional real euclidean space the first version essentially having been introduced around the same time by ben said and orsted and independently by soltani and the dunkl heat kernel due to rosler of the dunkl laplacian associated with the same coxeter group all but one of our relations are originally due to hall in the context of standard segal bargmann analysis on euclidean space hall s results trivial dunkl structure and arbitrary finite dimension as well as our own results in deformed quantum mechanics non trivial dunkl structure dimension one are particular cases of the results proved here so we can understand all of these versions of the segal bargmann transform associated to a coxeter group as hall type transforms in particular we define an analogue of hall s version c generalized segal bargmann transform which is then shown to be dunkl convolution with the dunkl heat kernel followed by analytic continuation in the context of version c we also introduce a new segal bargmann space and a new transform associated to the dunkl theory also we have what appears to be a new relation in this context between the segal bargmann kernels for versions a and c

infinite horizon stable predictive control terminal constraints guarantee the stability of predicted trajectories and form the basis of predictive control algorithms with guaranteed stability earlier work in the literature uses terminal constraints which define sufficient but not necessary conditions for the stability of predicted trajectories in this paper we deploy conditions which are both necessary and sufficient and hence release more degrees of freedom for optimizing performance and or meeting constraints also an alternative means of computing the implied infinite horizon gpc cost avoiding the need for solving a lyapunov equation is presented

a maximum principle applied to quasi geostrophic equations we study the initial value problem for dissipative 2d quasi geostrophic equations proving local existence global results for small initial data in the super critical case decay of lp norms and asymptotic behavior of viscosity solution in the critical case our proofs are based on a maximum principle valid for more general flows

brief infinite horizon predictive control of constrained continuous time linear systems this paper considers receding horizon control strategies for constrained linear systems continuous time predictions of input output responses on an infinite horizon allow exploitation of the full range of plant behaviour in addition an infinite prediction horizon ensures the nominal stability of the receding horizon control law the problem of optimizing predictions subject to constraints is made tractable through the use of a finite dimensional prediction class and by minimizing prediction costs at discrete instants necessary and sufficient conditions on the prediction class are derived using input output stability theory and the controller structure further refined on the basis of a criterion for ensuring feasibility in a receding horizon sense constrained optimization is performed using quadratic programming

global unique solvability of nonhomogeneous asymmetric fluids a lagrangian approach abstract we show global existence and uniqueness of solutions for the 3d nonhomogeneous asymmetric fluids equations through a lagrangian approach in particular uniqueness of the solution is proved under quite soft assumptions about its regularity which brings the knowledge about nonhomogeneous asymmetric fluids to the same level as for the variable density navier stokes equations

regularity criterion for a critical fractional diffusion model of two dimensional micropolar flows abstract this paper is devoted to the beale kato majda bkm regularity criterion of the 2d micropolar equations in the critical fractional diffusion situation 1 for 0 and 0 with the use of the littlewood paley theory the global existence of the unique solution u w to the equations is found to be completely determined by the velocity field u the dynamical behaviour of the scalar angular velocity w is controlled by the velocity u more precisely it is shown that the strong solution u w exists globally if 0 t u l 2 d for any t

global well posedness to the cauchy problem of 2d density dependent micropolar equations with large initial data and vacuum abstract this paper studies the cauchy problem of the 2d nonhomogeneous incompressible micropolar equations it is shown that the problem admits a unique global strong solution note that the initial data can be arbitrary large and the initial density can contain vacuum states

vanishing viscosity for non homogeneous asymmetric fluids in r3 the l2 case abstract we study the vanishing viscosity problem for the local in time solutions to the equations of non homogeneous viscous incompressible asymmetric fluid in r 3 in the l 2 context we prove that the fluid variables converge uniformly as the viscosities go to zero to a solution of a non homogeneous non viscous incompressible asymmetric fluid governed by an euler like system this completes the previous work 5 where results for l p p 3 where obtained

singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids many interesting problems in classical physics involve the limiting behavior of quasilinear hyperbolic systems as certain coefficients become infinite using classical methods the authors develop a general theory of such problems this theory is broad enough to study a wide variety of interesting singular limits in compressible fluid flow and magneto fluid dynamics including new constructive local existence theorems for the time singular limit equations in particular the authors give an entirely self contained classical proof of the convergence of solutions of the compressible fluid equations to their incompressible limits as the mach number becomes small the theory depends upon a balance between certain inherently nonlinear structural conditions on the matrix coefficients of the system together with appropriate initialization procedures similar results are developed also for the compressible and incompressible navier stokes equations with periodic initial data independent of the viscosity coefficients as they tend to zero

global well posedness and large time decay for the 2d micropolar equations abstract this paper studies the global in time regularity and large time behavior of solutions to the 2d micropolar equations with only angular viscosity dissipation micropolar equations model a class of fluids with nonsymmetric stress tensor such as fluids consisting of particles suspended in a viscous medium when there is no kinematic viscosity in the momentum equation the global regularity problem is not easy due to the lack of suitable bounds on the derivatives the idea here is to fully exploit the structure of the system and control the vorticity via the evolution equation of a combined quantity of the vorticity and the micro rotation angular velocity to understand the large time behavior we overcome two main difficulties the lack of kinematic viscosity and the presence of linear terms classical tools such as the fourier splitting method of schonbek and kato s approach for the decay of small solutions do not apply here we introduce a diagonalization process to eliminate the linear terms and rely on the uniform bounds for the first derivatives of the solutions to generate suitable decay rates

fast suboptimal predictive control with guaranteed stability efficient algorithms for constrained minimization of infinite horizon predictive control costs are presented control laws with guaranteed stability and asymptotic tracking are derived on the basis of appropriately chosen one dimensional and ellipsoidal constraint set approximations these achieve comparable performance with existing qp based control laws with significant reductions in computational burden

the critical sobolev inequalities in besov spaces and regularity criterion to some semi linear evolution equations we show the critical sobolev inequalities in the besov spaces with the logarithmic form such as brezis gallouet wainger and beale kato majda as an application of those inequalities the regularity problem under the critical condition to the navier stokes equations the euler equations in mathbb r n and the gradient flow to the harmonic map to the sphere are discussed namely the serrin ohyama type regularity criteria are improved in the terms of the besov spaces

global well posedness for the 2d boussinesq system with anisotropic viscosity and without heat diffusion abstract we establish global existence and uniqueness theorems for the two dimensional non diffusive boussinesq system with anisotropic viscosity acting only in the horizontal direction which arises in ocean dynamics models global well posedness for this system was proven by danchin and paicu however an additional smoothness assumption on the initial density was needed to prove uniqueness they stated that it is not clear whether uniqueness holds without this additional assumption the present work resolves this question and we establish uniqueness without this additional assumption furthermore the proof provided here is more elementary we use only tools available in the standard theory of sobolev spaces and without resorting to para product calculus we use a new approach by defining an auxiliary stream function associated with the density analogous to the stream function associated with the vorticity in 2d incompressible euler equations then we adapt some of the ideas of yudovich for proving uniqueness for 2d euler equations

global weak solutions for variable density asymmetric incompressible fluids abstract we establish the existence of global in time weak solutions for the equations of asymmetric incompressible fluids with variable density when the initial density is not necessarily strictly positive

generalized hermite polynomials and the heat equation for dunkl operators based on the theory of dunkl operators this paper presents a general concept of multivariable hermite polynomials and hermite functions which are associated with finite reflection groups on n the definition and properties of these generalized hermite systems extend naturally those of their classical counterparts partial derivatives and the usual exponential kernel are here replaced by dunkl operators and the generalized exponential kernel k of the dunkl transform in the case of the symmetric group s n our setting includes the polynomial eigenfunctions of certain calogero sutherland type operators the second part of this paper is devoted to the heat equation associated with dunkl s laplacian as in the classical case the corresponding cauchy problem is governed by a positive one parameter semigroup this is assured by a maximum principle for the generalized laplacian the explicit solution to the cauchy problem involves again the kernel k which is on the way proven to be nonnegative for real arguments

global well posedness of the 2d boussinesq equations with fractional laplacian dissipation abstract as a continuation of the previous work 48 in this paper we focus on the cauchy problem of the two dimensional 2d incompressible boussinesq equations with fractional laplacian dissipation we give an elementary proof of the global regularity of the smooth solutions of the 2d boussinesq equations with a new range of fractional powers of the laplacian the argument is based on the nonlinear lower bounds for the fractional laplacian established in 13 consequently this result significantly improves the recent works 13 45 48

some new examples of markov processes which enjoy the time inversion property in this paper we give a sufficient condition on the semi group densities of an homogeneous markov process taking values in n which ensures that it enjoys the time inversion property our condition covers all previously known examples of markov processes satisfying this property as new examples we present a class of markov processes with jumps the dunkl processes and their radial parts

global regularity for the 2d boussinesq equations with partial viscosity terms abstract in this paper we prove the global in time regularity for the 2d boussinesq system with either the zero diffusivity or the zero viscosity we also prove that as diffusivity viscosity tends to zero the solutions of the fully viscous equations converge strongly to those of zero diffusion viscosity equations our result for the zero diffusion system in particular solves the problem no 3 posed by moffatt in r l ricca ed kluwer academic publishers dordrecht the netherlands 2001 pp 3 10

on the regularity criterion for three dimensional micropolar fluid flows in besov spaces abstract this paper studies the regularity criterion of weak solutions for three dimensional 3d micropolar fluid flows when the velocity field satisfies u l 2 1 r 0 t b r r 3 for 1 r 1 then the weak solution u w is regular on 0 t the methods are mainly based on the fourier localization technique and bony s para product decomposition

remarks on the breakdown of smooth solutions for the 3 d euler equations the authors prove that the maximum norm of the vorticity controls the breakdown of smooth solutions of the 3 d euler equations in other words if a solution of the euler equations is initially smooth and loses its regularity at some later time then the maximum vorticity necessarily grows without bound as the critical time approaches equivalently if the vorticity remains bounded a smooth solution persists

global well posedness for a smoluchowski equation coupled with navier stokes equations in 2d we prove global existence for a nonlinear smoluchowski equation a nonlinear fokker planck equation coupled with navier stokes equations in 2d the proof uses a deteriorating regularity estimate in the spirit of 5 see also 1

global regularity of the 2d micropolar fluid flows with zero angular viscosity abstract in this paper we prove the global existence and uniqueness of smooth solutions to the 2d micropolar fluid flows with zero angular viscosity

global regularity for the 2d magneto micropolar equations with partial and fractional dissipation abstract this paper studies two cases of global regularity problems on the 2d magneto micropolar equations with partial magnetic diffusion and fractional dissipation for the first case the velocity field is ideal the micro rotational velocity is with laplacian dissipation and the magnetic field has fractional partial diffusion 22 b 1 11 b 2 with 1 in the second case the velocity has a fractional laplacian dissipation u with any 0 the micro rotational velocity is with laplacian dissipation and the magnetic field has partial diffusion 22 b 1 11 b 2 in two cases the global well posedness of classical solutions is proved in this paper

global well posedness for 2d polymeric fluid models and growth estimate motivated by p constantin n masmoudi global well posedness for a smoluchowski equation coupled with navier stokes equations in 2d comm math phys 278 2008 179 191 f lin ping zhang zhifei zhang on the global existence of smooth solution to the 2 d fene dumbbell model comm math phys 277 2008 531 553 we prove the global existence of smooth solutions to a coupled microscopic macroscopic model for polymeric fluid in 2d under the co rotational assumption furthermore we provide an estimate on the time growth of these solutions our method is general and can be applied to the co rotational fene model and to the rod like model without the co rotational assumption c 2008 elsevier b v all rights reserved

irreducibility of the three and two and a half dimensional hall magnetohydrodynamics system abstract the hall magnetohydrodynamics system has been considered by many to play an important role in astrophysical plasmas star formation and magnetic re connection the hall term mathematically elevates the magnetohydrodynamics system from a semi linear to a quasi linear type and standard results which are well known for the navier stokes equations and the magnetohydrodynamics system such as the local well posedness in the non diffusive case as well as the uniqueness of the weak solution in case the solution depends only on two spatial variables are completely open for the hall magnetohydrodynamics system because the hall magnetohydrodynamics system is not known to be globally well posed even if the solution depends only on two spatial variables a typical method to prove ergodicity for the two dimensional navier stokes equations such as hairer and mattingly 2006 seems to have no chance in this manuscript we take advantage of the structure of the hall term follow the work of flandoli 1997 and prove its irreducibility property in order to elaborate on the effect of the hall term we also prove analogous results for related systems such as the magnetohydrodynamics system benard problem magnetic benard problem micropolar fluid system as well as the magneto micropolar fluid system at the time of writing this manuscript due to a technical difficulty the strong feller property of the hall magnetohydrodynamics system is an open problem

global well posedness for the micropolar fluid system in critical besov spaces abstract we prove the global well posedness for the 3 d micropolar fluid system in the critical besov spaces by making a suitable transformation of the solutions and using the fourier localization method especially combined with a new l p estimate for the green matrix to the linear system of the transformed equation this result allows to construct global solutions for a class of highly oscillating initial data of cannone s type meanwhile we analyze the long time behavior of the solutions and get some decay estimates

vanishing viscosity for non homogeneous asymmetric fluids in r3 we consider a non homogeneous viscous incompressible asymmetric fluid in r 3 we prove that there exists a small time interval where the fluid variables converge uniformly as the viscosities tend to zero in the limit we find a non homogeneous non viscous incompressible asymmetric fluid governed by an euler like system

on the global well posedness for boussinesq system abstract in this paper we give a global well posedness result for the two dimensional boussinesq system with partial viscosity when the initial data v 0 b 1 1 r 2 l 2 r 2 and 0 b 2 1 0 r 2

weak solutions with improved regularity for the nonhomogeneous asymmetric fluids equations with vacuum abstract we prove the existence of local and global in time weak solutions for the equations of nonhomogeneous incompressible asymmetric fluids in a bounded domain r 3 when the initial vacuum is allowed i e the initial density 0 is not necessarily strictly positive our solutions here are more regular than previous results and so satisfy the initial conditions in a stronger sense the global in time solutions are obtained under smallness assumptions on the initial data and forcing terms