global existence and optimal convergence rates for the strong solutions in h 2 to the 3d viscous liquid gas two phase flow model abstract this paper is concerned with the cauchy problem of the three dimensional viscous liquid gas two phase flow model we prove the global existence of a strong solution when h 2 norm of the initial perturbation around a constant state is sufficiently small and its l 1 norm is bounded moreover the optimal convergence rates are also obtained for such a solution

well posedness for compressible mhd systems with highly oscillating initial data in this paper a unique local solution for compressible magnetohydrodynamics systems has been constructed in the critical besov space framework by converting the system in euler coordinates to a system in lagrange coordinates our results improve the range of the lebesgue exponent in the besov space from 2 n to 2 2n where n denotes the space dimension then we give a lower bound for the maximal existence time which is important for our construction of global solutions based on the lower bound we use the effective viscous flux and hoff s energy method to obtain the unique global solution which allows the initial velocity field and the magnetic field to have large energies and allows the initial density to exhibit large oscillations on a set of small measure

a priori estimates for the 3d quasi geostrophic system abstract the present article is devoted to the 3d dissipative quasi geostrophic system qg this system can be obtained as a limit model of the primitive equations in the asymptotics of strong rotation and stratification and involves a non radial non local homogeneous pseudo differential operator of order 2 denoted by and whose semigroup kernel reaches negative values after a refined study of the non local part of we prove a priori estimates in the general l p setting for the 3d qg model the main difficulty of this article is to study this highly non classical operator and the commutator of with a lagrangian change of variable an important application of these a priori estimates providing bound from below to the lifespan of the solutions of the primitive equations for ill prepared blowing up initial data can be found in a companion paper

rational irreducible characters and rational conjugacy classes in finite groups we prove that a finite group g has two rational valued irreducible characters if and only if it has two rational conjugacy classes and determine the structure of any such group along the way we also prove a conjecture of gow stating that any finite group of even order has a non trivial rational valued irreducible character of odd degree

on the well posedness of the full compressible navier stokes system in critical besov spaces abstract we are concerned with the cauchy problem of the full compressible navier stokes equations satisfied by viscous and heat conducting fluids in r n we focus on the so called critical besov regularity framework in this setting it is natural to consider initial densities 0 velocity fields u 0 and temperatures 0 with a 0 0 1 b p 1 n p u 0 b p 1 n p 1 and 0 b p 1 n p 2 after recasting the whole system in lagrangian coordinates and working with the total energy along the flow rather than with the temperature we discover that the system may be solved by means of banach fixed point theorem in a critical functional framework whenever the space dimension is n 2 and 1 p 2 n back to eulerian coordinates this allows to improve the range of p s for which the system is locally well posed compared to 7

the large time behavior of solutions in the critical l p framework for compressible viscous and heat conductive gas flows in this paper we are concerned with non isentropic navier stokes equations governing compressible viscous and heat conductive gases we formulate an additional regularity assumption of low frequencies in rd d 3 and then establish the sharp time weighted inequality which allows us to get the time decay estimates of global strong solutions in the lp critical besov spaces precisely it is shown that if the initial data belong to some besov space b2 s1 with s1 1 d2 s0 s0 2dp d2 then the lp norm of the critical global solutions admits the time decay t s12 d2 12 1p in particular t d2p if s1 s0 which coincides with that of the heat kernel in the lp framework in comparison with the work of danchin and xu j math fluid mech 20 1641 1665 2018 the low frequency assumption is improved such that the regularity s1 belongs to the whole range 1 d2 s0

on some decay properties of stokes semigroup of compressible viscous fluid flow in a 2 dimensional exterior domain in this paper we proved the local energy decay and some lp lq decay properties of solutions to the initial boundary value problem for the stokes equations of compressible viscous fluid flow in a 2 dimensional exterior domain kobayashi 1997 19 and kobayashi and shibata 1999 21 treated the same problem in a 3 dimensional exterior domain and our results obtained in this paper are an extension of results in kobayashi 1997 19 and kobayashi and shibata 1999 21 to the 2 dimensional case the fundamental solution to the resolvent equations for the stokes equations in r2 has a logarithmical singularity at 0 being a resolvent parameter while it is continuous up to 0 in r3 this difference requires us a new idea to prove the local energy decay estimate once getting the local energy decay estimate the required lp lq decay estimates in the exterior domain are obtained by combining the local energy estimate and the lp lq estimates in r2 by a cut off technique

global regularity for some classes of large solutions to the navier stokes equations in previous works by the first two authors classes of initial data to the three dimensional incompressible navier stokes equations were presented generating a global smooth solution although the norm of the initial data may be chosen arbitrarily large the main feature of the initial data considered in one of those studies is that it varies slowly in one direction though in some sense it is well prepared its norm is large but does not depend on the slow parameter the aim of this article is to generalize that setting to an ill prepared situation the norm blows up as the small parameter goes to zero as in those works the proof uses the special structure of the nonlinear term of the equation

a reduction theorem for the mckay conjecture the mckay conjecture asserts that for every finite group g and every prime p the number of irreducible characters of g having p degree is equal to the number of such characters of the normalizer of a sylow p subgroup of g although this has been confirmed for large numbers of groups including for example all solvable groups and all symmetric groups no general proof has yet been found in this paper we reduce the mckay conjecture to a question about simple groups we give a list of conditions that we hope all simple groups will satisfy and we show that the mckay conjecture will hold for a finite group g if every simple group involved in g satisfies these conditions also we establish that our conditions are satisfied for the simple groups psl2 q for all prime powers q 4 and for the suzuki groups sz q and ree groups r q where q 2 e or q 3 e respectively and e 1 is odd since our conditions are also satisfied by the sporadic simple group j 1 it follows that the mckay conjecture holds for all primes p for every finite group having an abelian sylow 2 subgroup

a low frequency assumption for optimal time decay estimates to the compressible navier stokes equations the global existence issue in critical spaces for compressible navier stokes equations was addressed by danchin invent math 141 579 614 2000 and then developed by charve and danchin arch rational mech anal 198 233 271 2010 chen et al commun pure appl math 63 1173 1224 2010 and haspot arch rational mech anal 202 427 460 2011 in more general lp setting the main aim of this paper is to exhibit more precisely time decay estimates of solutions constructed in the critical regularity framework to the best of our knowledge the low frequency assumption usually plays a key role in the large time asymptotics of solutions which was firstly observed by matsumura and nishida j math kyoto univ 20 67 104 1980 in the l 1 mathbb r d space we now claim a new low frequency assumption for barotropic compressible navier stokes equations which may be of interest in the mathematical analysis of viscous fluids precisely if the initial density and velocity additionally belong to some besov space dot b sigma 1 2 infty mathbb r d with the regularity sigma 1 in 1 d 2 2d p d 2 then a sharp time weighted inequality including enough time decay information can be available where optimal decay exponents for the high frequencies are exhibited the proof mainly depends on some non standard besov product estimates as a by product those optimal time decay rates of lq lr type are also captured in the critical framework

a sharp time weighted inequality for the compressible navier stokes poisson system in the critical l p framework abstract the compressible navier stokes poisson system takes the form of usual navier stokes equations coupled with the self consistent poisson equation which is used to simulate the transport of charged particles under the electrostatic potential force in this paper we focus on the large time behavior of global strong solutions in the l p critical besov spaces inspired by the dissipative effect arising from poisson potential we formulate a new regularity assumption of low frequencies and then establish the sharp time weighted inequality which leads to the optimal time decay estimates of strong solutions indeed we see that the decay of density is faster at the half rate than that of velocity which is a different ingredient in comparison with the situation of compressible navier stokes equations our proof mainly depends on tricky and non classical besov product estimates with respect to various sobolev embeddings

global strong solution for the density dependent incompressible viscoelastic fluids in the critical lp framework abstract in this paper we consider the cauchy problem of the density dependent incompressible viscoelastic fluids in the whole space r d d 2 with the initial data close to a stable equilibrium this work is dedicated to deriving the existence result of the global strong solution in the critical space with respect to the natural scaling of the equations in the l p framework

well posedness and time decay for compressible viscoelastic fluids in critical besov space abstract in this paper we construct local solution with highly oscillating initial velocity and then get the global strong solution in the l p based besov space which improves the result of j qian z zhang 2010 25 and x hu d wang 2011 14 the local existence and uniqueness lies on the lagrange coordinate transform and the contraction mapping theorem the global result lies on a decomposition of the system and some commutator estimates in the last part we prove a time decay in the critical besov space framework which seems to have little investigation the proof is based on the properties of the green s matrix and various interpolations between besov type spaces

global strong solutions for equations related to the incompressible viscoelastic fluids with a class of large initial data abstract we investigate the global strong solutions for a system related to the incompressible viscoelastic fluids of oldroyd b type with a class of large initial data e 0 e 0 i j n n v 0 v 01 v 0 n we obtain the global existence and uniqueness of a solution provided that e 0 h v 0 h are sufficiently small in b 2 1 n 2 1 b 2 1 n 2 b 2 1 n 2 1 while e 0 n and v 0 n are large where e 0 h e 0 i j n 1 n v 0 h v 01 v 0 n 1 and e 0 n e 0 n 1 e 0 n n

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

the cauchy problem for the compressible navier stokes equations in the l p framework the global in time existence of regular solutions to the compressible navier stokes equations in the whole space is obtained the solutions are close to nontrivial equilibrium solutions moreover the result is sharp in the lp framework the velocity of the fluid belongs to wr2 1 and the initial density to w1r with r 3

existence of global strong solutions in critical spaces for barotropic viscous fluids this paper is dedicated to the study of viscous compressible barotropic fluids in dimension n 2 we address the question of the global existence of strong solutions for initial data close to a constant state having critical besov regularity first this article shows the recent results of charve and danchin arch ration mech anal 198 1 233 271 2010 and chen et al commun pure appl math 63 1173 1224 2010 with a new proof our result relies on a new a priori estimate for the velocity that we derive via the intermediary of the effective velocity which allows us to cancel out the coupling between the density and the velocity as in haspot well posedness in critical spaces for barotropic viscous fluids 2009 second we improve the results of charve and danchin 2010 and chen et al 2010 by adding as in charve and danchin 2010 some regularity on the initial data in low frequencies in this case we obtain global strong solutions for a class of large initial data which rely on the results of hoff arch rational mech anal 139 303 354 1997 hoff commun pure appl math 55 11 1365 1407 2002 and hoff j math fluid mech 7 3 315 338 2005 and those of charve and danchin 2010 and chen et al 2010 we conclude by generalizing these results for general viscosity coefficients

optimal decay rates of isentropic compressible navier stokes equations with discontinuous initial data abstract the global in time solutions with discontinuous initial data when the density has no regularity are constructed in 10 11 12 for the isentropic compressible navier stokes equations in multi dimensional spaces the time decay rates of these solutions with low regularity still remain unsolved in this paper we establish the decay rates of solutions in 10 11 12 in l r norm with 2 r and the decay rate of the first order derivative of the velocity in l 2 norm when the initial data are bounded in l 1 the optimal decay rates are also obtained these decay rates are the same as rates for classical solutions in 18 20

fault reconstruction for takagi sugeno fuzzy systems via learning observers abstractthis paper addresses the problem of observer based fault reconstruction for takagi sugeno fuzzy systems two types of fuzzy learning observers are constructed to achieve simultaneous reconstruction of system states and actuator faults stability and convergence of the proposed observers are proved using lyapunov stability theory and necessary conditions for the existence of the observers are further discussed the design of fuzzy learning observers can be formulated in terms of a series of linear matrix inequalities that can be conveniently solved using convex optimisation technique a single link flexible manipulator is employed to verify the effectiveness of the proposed fault reconstructing approaches

well posedness in critical spaces for the system of compressible navier stokes in larger spaces this paper is dedicated to the study of viscous compressible barotropic fluids in dimension n geq2 we address the question of well posedness for it large data having critical besov regularity our result improves the analysis of r danchin in cite dw of chen et al in cite c2 and of the author in cite h1 h2 inasmuch as we may take initial density in b nn p 1 with 1 leq p infty our result relies on a new a priori estimate for the velocity where we introduce a new unknown called textit effective velocity to weaken one the coupling between the density and the velocity in particular for the first time we obtain uniqueness without imposing hypothesis on the gradient of the density

global well posedness of compressible navier stokes equations for some classes of large initial data we prove the global well posedness of three dimensional compressible navier stokes equations for some classes of large initial data which may have large oscillation for the density and large energy for the velocity the proof uses the special structure of the system especially the effective viscous flux

on the solvability of the constrained lyapunov problem this paper considers system theoretic conditions for the solvability of the so called constrained lyapunov problem for nonsquare systems these problems commonly appear in the control systems literature both a static output feedback problem and an observer problem are considered the basis for the work described in this paper is a new canonical form that simplifies the analysis and deals with the equality constraint in a simple way

representations of finite special linear groups in non defining characteristic we classify irreducible modules over the finite special linear group sln q in the non defining characteristic l describe restrictions of irreducible modules from gln q to sln q classify complex irreducible characters of sln q irreducible modulo l and discuss unitriangularity of the l decomposition matrix for sln q

the initial value problem for the compressible navier stokes equations without heat conductivity abstract in this paper we are concerned with the global existence and convergence rates of strong solutions for the compressible navier stokes equations without heat conductivity in r 3 the global existence and uniqueness of strong solutions are established by the delicate energy method under the condition that the initial data are close to the constant equilibrium state in h 2 framework furthermore if additionally the initial data belong to l 1 the optimal convergence rates of the solutions in l 2 norm and convergence rates of their spatial derivatives in l 2 norm are obtained

the incompressible limit for compressible mhd equations in lp type critical spaces abstract in this paper the global well posedness and the low mach number limit for compressible viscous magnetohydrodynamic equations in the critical l p type besov space are considered more precisely we will show that in the isentropic case the solution of compressible magnetohydrodynamic equations will converge to that of incompressible magnetohydrodynamic equations when the mach number tends to zero in the critical l p framework moreover the convergence rate will be obtained

on a lagrangian method for the convergence from a non local to a local korteweg capillary fluid model in the present article we are interested in further investigations for the barotropic compressible navier stokes system endowed with a non local capillarity we studied in 7 thanks to an accurate study of the associated linear system using a lagrangian change of coordinates we provide more precise energy estimates in terms of hybrid besov spaces naturally depending on a threshold frequency which is determined in function of the physical parameter distinguishing the low and the high regimes it allows us in particular to prove the convergence of the solutions from the non local to the local korteweg system another mathematical interest of this article is the study of the effect of the lagrangian change on the non local capillary term

fuzzy model based fault tolerant design for nonlinear stochastic systems against simultaneous sensor and actuator faults this paper addresses the problem of fault estimation and fault tolerant control for a class of takagi sugeno t s fuzzy ito stochastic systems subject to simultaneously sensor and actuator faults the main difficulty in this study is that sensor faults actuator faults and stochastic noise that are governed by brownian motion are taken into simultaneous consideration in a unified framework and traditional fault tolerant approaches are not effective to solve this research issue a new descriptor fuzzy sliding mode observer approach is presented in this paper to obtain the simultaneous estimates of system state sensor fault and actuator fault vectors based on the state estimates an observer based fault tolerant control ftc scheme is developed to stabilize the resulting closed loop system finally a simulation example is provided to show the effectiveness of the proposed fault tolerant approach

a geometric approach to nonlinear fault detection and isolation we present a differential geometric approach to the problem of fault detection and isolation for nonlinear systems a necessary condition for the problem to be solvable is derived in terms of an unobservability distribution which is computable by means of suitable algorithms the existence and regularity of such a distribution implies the existence of changes of coordinates in the state and in the output space which induce an observable quotient subsystem unaffected by all fault signals but one for this subsystem a fault detection filter is designed

h sub spl infin design with pole placement constraints an lmi approach this paper addresses the design of state or output feedback h sub spl infin controllers that satisfy additional constraints on the closed loop pole location sufficient conditions for feasibility are derived for a general class of convex regions of the complex plane these conditions are expressed in terms of linear matrix inequalities lmis and the authors formulation is therefore numerically tractable via lmi optimization in the state feedback case mixed h sub 2 h sub spl infin synthesis with regional pole placement is also discussed finally the validity and applicability of this approach are illustrated by a benchmark example

equivariance and extendibility in finite reductive groups with connected center we show that several character correspondences for finite reductive groups g are equivariant with respect to group automorphisms under the additional assumption that the linear algebraic group associated to g has connected center the correspondences we consider are the so called jordan decomposition of characters introduced by lusztig and the generalized harish chandra theory of unipotent characters due to broue malle michel in addition we consider a correspondence giving character extensions due to the second author in order to verify the inductive mckay condition from isaacs malle navarro for the non abelian finite simple groups of lie types 3 mathsf d 4 mathsf e 8 mathsf f 4 2 mathsf f 4 and mathsf g 2

a global existence result for the compressible navier stokes equations in the critical l p framework the present paper is dedicated to the global well posedness issue for the barotropic compressible navier stokes system in the whole space mathbb r d with d 2 we aim at extending the work by danchin inventiones mathematicae 141 3 579 614 2000 to a critical framework which is not related to the energy space for small perturbations of a stable equilibrium state in the sense of suitable lp type besov norms we establish the global existence as a consequence like for incompressible flows one may exhibit a class of large highly oscillating initial velocity fields for which global existence and uniqueness holds true in passing we obtain new estimates for the linearized and the paralinearized systems which may be of interest for future works on compressible flows

local in time results for local and non local capillary navier stokes systems with large data abstract in this article we study three capillary compressible models the classical local navier stokes korteweg system and two non local models for large initial data bounded away from zero and with a reference pressure state which is not necessarily stable p can be non positive we prove that these systems have a unique local in time solution and we study the convergence rate of the solutions of the non local models towards the local korteweg model the results are given for constant viscous coefficients and we explain how to extend them for density dependant coefficients

global existence of strong solution for viscous shallow water system with large initial data on the irrotational part abstract we are interested in studying the cauchy problem for the viscous shallow water system in dimension n 2 we show the existence of global strong solutions with large initial data on the irrotational part of the velocity for the scaling of the equations more precisely our smallness assumption on the initial data is supercritical for the scaling of the equations it allows us to give a first kind of answer to the problem of the existence of global strong solution with large initial energy data in dimension n 2 to do this we introduce the notion of quasi solutions which consists in solving the pressureless viscous shallow water system we can obtain such solutions at least for irrotational data which are subject to regularizing effects both on the velocity and on the density this smoothing effect is purely nonlinear and is crucial in order to build solution of the viscous shallow water system as perturbations of the quasi solutions indeed the pressure term can be considered as a remainder term which becomes small in high frequencies for the scaling of the equations to finish we prove the existence of global strong solution with large initial data when n 2 provided that the mach number is sufficiently large

dispersive effect and global well posedness of the compressible viscoelastic fluids abstract this paper is concerned with the global well posedness issue of the compressible viscoelastic fluids in the whole space r n n 2 the proof relies on the dispersive estimates to the linearized hyperbolic system combined with energy estimates to the hyperbolic parabolic system by exploiting the intrinsic structure of the system under some physical restrictions we find that the compressible viscoelastic fluids admits a unique global solution with a class of large initial data in the sense of critical l 2 framework

state and input estimation for a class of uncertain systems we consider here the problem of state and input estimation for a class of uncertain systems which consist of a nominally linear part and an uncertain nonlinear time varying part which can be regarded as a state dependent time varying input we obtain a lyapunov type characterization of the assumptions commonly found in the literature on this problem using this characterization we obtain estimators which using only a measured output can asymptotically estimate to any desired accuracy the system state and the input

optimal decay rate for the compressible navier stokes poisson system in the critical l p framework abstract in this paper we consider the large time behavior of global solutions to the initial value problem for the compressible navier stokes poisson system in the l p critical framework and in any dimension n 3 we obtain the time decay rates not only for lebesgue spaces but also for a family of besov norms with negative or nonnegative regularity exponents which improves the decay results in high sobolev regularity the proof is mainly based on the littlewood paley theory and refined time weighted inequalities in fourier space

robust observer design for unknown inputs takagi sugeno models this paper deals with the observer design for takagi sugeno t s fuzzy models subject to unknown inputs and disturbance affecting both states and outputs of the system sufficient conditions to design an unknown input t s observer are given in linear matrix inequality lmi terms both continuous time and discrete time cases are studied relaxations are introduced by using intermediate variables extension to the case of unmeasured decision variables is also given a numerical example is given to illustrate the effectiveness of the given results

global existence in critical spaces for compressible navier stokes equations we investigate global strong solutions for isentropic compressible fluids with initial data close to a stable equilibrium we obtain the existence and uniqueness of a solution in a functional setting invariant by the scaling of the associated equations more precisely the initial velocity has the same critical regularity index as for the incompressible homogeneous navier stokes equations and one more derivative is needed for the density we point out a smoothing effect on the velocity and a l 1 decay on the difference between the density and the constant reference state the proof lies on uniform estimates for a mixed hyperbolic parabolic linear system with a convection term

optimal time decay estimates for the compressible navier stokes equations in the critical l p framework the global existence issue for the isentropic compressible navier stokes equations in the critical regularity framework was addressed in danchin invent math 141 3 579 614 2000 more than 15 years ago however whether optimal time decay rates could be shown in critical spaces has remained an open question here we give a positive answer to that issue not only in the l2 critical framework of danchin invent math 141 3 579 614 2000 but also in the general lp critical framework of charve and danchin arch ration mech anal 198 1 233 271 2010 chen et al commun pure appl math 63 9 1173 1224 2010 haspot arch ration mech anal 202 2 427 460 2011 we show that under a mild additional decay assumption that is satisfied if for example the low frequencies of the initial data are in l p 2 mathbb r d the lp norm the slightly stronger dot b 0 p 1 norm in fact of the critical global solutions decays like t d frac 1p frac14 for t to infty exactly as firstly observed by matsumura and nishida in proc jpn acad ser a 55 337 342 1979 in the case p 2 and d 3 for solutions with high sobolev regularity

global solution to the incompressible oldroyd b model in the critical l p framework the case of the non small coupling parameter this paper is dedicated to the global well posedness issue of the incompressible oldroyd b model in the whole space mathbb r d with d geqq 2 it is shown that this set of equations admits a unique global solution in a certain critical lp type besov space provided that the initial data but not necessarily the coupling parameter is small enough as a consequence even through the coupling effect between the equations of velocity u and the symmetric tensor of constrains is not small one may construct the unique global solution to the oldroyd b model for a class of large highly oscillating initial velocity the proof relies on the estimates of the linearized systems of u and u mathbb p rm div tau which may be of interest for future works this result extends the work by chemin and masmoudi siam j math anal 33 84 112 2001 to the non small coupling parameter case

the incompressible limit in l p type critical spaces this paper aims at justifying the low mach number convergence to the incompressible navier stokes equations for viscous compressible flows in the ill prepared data case the fluid domain is either the whole space or the torus a number of works have been dedicated to this classical issue all of them being to our knowledge related to l 2 spaces and to energy type arguments in the present paper we investigate the low mach number convergence in the l p type critical regularity framework more precisely in the barotropic case the divergence free part of the initial velocity field just has to be bounded in the critical besov space dot b d p 1 p r cap dot b 1 infty 1 for some suitable p r in 2 4 times 1 infty we still require l 2 type bounds on the low frequencies of the potential part of the velocity and on the density though an assumption which seems to be unavoidable in the ill prepared data framework because of acoustic waves in the last part of the paper our results are extended to the full navier stokes system for heat conducting fluids