large time behavior of solutions to the compressible navier stokes equations around a parallel flow in a cylindrical domain abstract stability of parallel flow of the compressible navier stokes equation in a cylindrical domain is studied it is shown that if the reynolds and mach numbers are sufficiently small then parallel flow is asymptotically stable and the asymptotic leading part of the disturbances is described by a one dimensional viscous burgers equation

zappa szep products of semigroups and their c algebras abstract zappa szep products of semigroups provide a rich class of examples of semigroups that include the self similar group actions of nekrashevych we use li s construction of semigroup c algebras to associate a c algebra to zappa szep products and give an explicit presentation of the algebra we then define a quotient c algebra that generalises the cuntz pimsner algebras for self similar actions we indicate how known examples previously viewed as distinct classes fit into our unifying framework we specifically discuss the baumslag solitar groups the binary adding machine the semigroup n n and the a x b semigroup z z

weak type 1 1 inequalities and regularity properties of adjoint and normalized adjoint solutions to linear nondivergence form operators with vmo coefficients

decay estimates of solutions for the equations of motion of compressible viscous and heat conductive gases in an exterior domain in ℝ3 we consider the equations of motion of compressible viscous and heat conductive gases in an exterior domain in 3 we give the l q l p estimates for solutions to the linearized equations and show an optimal decay estimate for solutions to the nonlinear problem

global existence of solutions to the compressible navier stokes equation around parallel flows abstract the initial boundary value problem for the compressible navier stokes equation is considered in an infinite layer of r n it is proved that if n 3 then strong solutions to the compressible navier stokes equation around parallel flows exist globally in time for sufficiently small initial perturbations provided that the reynolds and mach numbers are sufficiently small the proof is given by a variant of the matsumura nishida energy method based on a decomposition of solutions associated with a spectral property of the linearized operator

normalizers and permutative endomorphisms of the 2 adic ring c algebra abstract a complete description is provided for the unitary normalizer of the diagonal cartan subalgebra d 2 in the 2 adic ring c algebra q 2 which generalizes and unifies analogous results for cuntz and bunce deddens algebras furthermore the inclusion o 2 q 2 is proved not to be regular finally countably many novel permutative endomorphisms of q 2 are exhibited with prescribed images of the generator u

boundary quotients of c algebras of right lcm semigroups abstract we study c algebras associated to right lcm semigroups that is semigroups which are left cancellative and for which any two principal right ideals are either disjoint or intersect in another principal right ideal if p is such a semigroup its c algebra admits a natural boundary quotient q p we show that q p is isomorphic to the tight c algebra of a certain inverse semigroup associated to p and thus is isomorphic to the c algebra of an etale groupoid we use this to give conditions on p which guarantee that q p is simple and purely infinite and give applications to self similar groups and zappa szep products of semigroups

low pass filters and representations of the baumslag solitar group we analyze representations of the baumslag solitar group bs 1 n u t utu 1 t n that admit wavelets and show how such representations can be constructed from a given low pass filter we describe the direct integral decomposition for some examples and derive from it a general criterion for the existence of solutions for scaling equations as another application we construct a fourier transform for some hausdorff measures

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

asymptotic behavior of solutions to the compressible navier stokes equation around a parallel flow the initial boundary value problem for the compressible navier stokes equation is considered in an infinite layer of mathbf r 2 it is proved that if the reynolds and mach numbers are sufficiently small then strong solutions to the compressible navier stokes equation around parallel flows exist globally in time for sufficiently small initial perturbations the large time behavior of the solution is described by a solution of a one dimensional viscous burgers equation the proof is given by a combination of spectral analysis of the linearized operator and a variant of the matsumura nishida energy method

on large time behavior of solutions to the compressible navier stokes equations in the half space in r3 the navier stokes equation for compressible viscous fluid is considered on the half space in r3 under the zero dirichlet boundary condition for the momentum with initial data near an arbitrarily given equilibrium of positive constant density and zero momentum time decay properties in l2 norms for solutions of the linearized problem are investigated to obtain the rate of convergence in l2 norms of solutions to the equilibrium when initial data are sufficiently close to the equilibrium in some lower bounds are derived for solutions to the linearized problem one of which indicates a nonlinear phenomenon not appearing in the case of the cauchy problem on the whole space

rate of convergence of non stationary flow to the steady flow of compressible viscous fluid we consider a compressible viscous fluid affected by external forces of general form which are small and smooth enough in suitable norms in r 3 in shibata and tanaka y shibata k tanaka on the steady flow of compressible viscous fluid and its stability with respect to initial disturbance j math soc japan 55 2003 797 826 we proved the unique existence and some regularity of the steady flow and its globally in time stability with respect to a small initial disturbance in the h 3 framework in this paper we investigate the rate of the convergence of the non stationary flow to the corresponding steady flow when the initial data are small enough in the h 3 and also belong to l 6 5

weighted poincare and sobolev inequalities and estimates for weighted peano maximal functions 1 introduction in this paper we derive local poincare and sobolev inequalities involving two weight functions the estimates we obtain include those proved by fabes kenig and serapioni in 8 for the one weight function case we also consider the notion of weighted peano derivatives and show that the peano derivative formed with a given weight function can be estimated in terms of a maximal function involving a second weight function in the special case of ordinary lebesgue measure results of this kind lead to the theorems of a p calderon and a zygmund about local differentiability of functions in sobolev spaces and of functions which are of bounded variation in the sense of tonelli see 3 and 4 all our results are based on variants of the basic estimate in 5 but we do not presuppose any facts from 5 let v x be a weight function on r i e let v x be nonnegative and locally integrable with respect to lebesgue measure we shall use the notation v e se v x dx ordinary lebesgue measure will be denoted ie l if bh x is the open ball with center x and radius h we say v satisfies the doubling condition with respect to lebesgue measure if

semigroup crossed products and the toeplitz algebras of nonabelian groups abstract we consider the quasi lattice ordered groups g p recently introduced by nica we realise their universal toeplitz algebra as a crossed product b p p by a semigroup of endomorphisms and show that the toeplitz representation is faithful precisely when an amenability condition is satisfied we then show directly that many interesting free products are amenable the final result contains theorems of cuntz and dinh on the uniqueness of toeplitz cuntz algebras as special cases

asymptotic behavior of solutions of the compressible navier stokes equations on the half space asymptotic behavior of solutions of the compressible navier stokes equations on the half space r n n 2 is considered around a given constant equilibrium a solution formula for the linearized problem is derived and l p estimates for solutions of the linearized problem are obtained for 2 p it is shown that as in the case of the cauchy problem the leading part of the solution of the linearized problem is decomposed into two parts one that behaves like diffusion waves and the other one purely diffusively there however are some aspects different from the cauchy problem especially in considering spatial derivatives it is also shown that the solution of the linearized problem approaches for large times the solution of the nonstationary stokes problem in some l p spaces and as a result a solution formula for the nonstationary stokes problem is obtained large time behavior of solutions of the nonlinear problem is then investigated in l p spaces for 2 p by applying the results on the linearized analysis and the weighted energy method the results indicate that there may be some nonlinear interaction phenomena not appearing in the cauchy problem

ring c algebras we associate reduced and full c algebras to arbitrary rings and study the inner structure of these ring c algebras as a result we obtain conditions for them to be purely infinite and simple we also discuss several examples originally our motivation comes from algebraic number theory

gradient estimates for a class of parabolic systems we establish local calderon zygmund type estimates for a class of parabolic problems whose model is the nonhomogeneous degenerate singular parabolic p laplacian system ut div du p 2du div f p 2f proving that f lqloc du lqloc q p we also treat systems with discontinuous coefficients of vanishing mean oscillation vmo type

on c 1 c 2 c2 and weak type 1 1 estimates for linear elliptic operators part ii we extend and improve the results in dong and kim commun partial differ equ 42 3 417 435 2017 showing that weak solutions to full elliptic equations in divergence form with zero dirichlet boundary conditions are continuously differentiable up to the boundary when the leading coefficients have dini mean oscillation and the lower order coefficients verify certain conditions similar results are obtained for non divergence form equations we extend the weak type 1 1 estimates in dong and kim commun partial differ equ 42 3 417 435 2017 and escauriaza duke math j 74 1 177 201 1994 up to the boundary and derive a harnack inequality for non negative adjoint solutions to non divergence form elliptic equations when the leading coefficients have dini mean oscillation

spectral properties of the linearized compressible navier stokes equation around time periodic parallel flow abstract the linearized problem around a time periodic parallel flow of the compressible navier stokes equation in an infinite layer is investigated by using the floquet theory spectral properties of the evolution operator associated with the linearized problem are studied in detail the floquet representation of a low frequency part of the evolution operator which plays an important role in the study of the nonlinear problem is obtained

the 2 adic ring c algebra of the integers and its representations abstract we study the 2 adic version of the ring c algebra of the integers first we work out the precise relation between the cuntz algebra o 2 and our 2 adic ring c algebra in terms of representations secondly we prove a 2 adic duality theorem identifying the crossed product arising from 2 adic affine transformations on the 2 adic numbers with the analogous crossed product algebra over the real numbers and finally as an outcome of this duality result we construct an explicit imprimitivity bimodule and prove that it transports one canonical representation into the other

a class of c algebras generalizing both graph algebras and homeomorphism c algebras iv pure infiniteness this is the final one in the series of papers where we introduce and study the c algebras associated with topological graphs in this paper we get a sufficient condition on topological graphs so that the associated c algebras are simple and purely infinite using this result we give one method to construct all kirchberg algebras as c algebras associated with topological graphs

stability of planar stationary solutions to the compressible navier stokes equation on the half space stability of planar stationary solutions to the compressible navier stokes equation on the half space bf r n n geq 2 under outflow boundary condition is investigated it is shown that the planar stationary solution is stable with respect to small perturbations in h s left bf r n right with s n 2 1 and the perturbations decay in l norm as t provided that the magnitude of the stationary solution is sufficiently small the stability result is proved by the energy method in the proof an energy functional based on the total energy of the system plays an important role

some estimates of solutions for the equations of motion of compressible viscous fluid in the three dimensional exterior domain abstract we consider the equations of motion of compressible viscous fluid in an exterior domain in r 3 we give the l q l p estimates for solutions to the linearized equations and show an optimal decay estimate for solutions to the nonlinear problem in particular we shall give l 1 estimates which implies the diffusion wave of compressible navier stokes flow

on the regularity theory of fully nonlinear parabolic equations ii recently m crandall and p l lions 3 developed a very successful method for proving the existence of solutions of nonlinear second order partial differential equations their method called the theory of viscosity solutions also applies to fully nonlinear equations in which even the second order derivatives can enter in nonlinear fashion solutions produced by the viscosity method are guaranteed to be continuous but not necessarily smooth here we announce smoothness results for viscosity solutions our methods extend those of 1 we obtain krylov safonov i e c estimates 8 c 1 schauder c and w estimates for viscosity solutions of uniformly parabolic equations in general form the results can be viewed as a priori estimates on the classical c solutions our method produces in particular regularity results for a broad new array of nonlinear heat equations including the bellman equation 6

initial boundary value problems for the equations of motion of compressible viscous and heat conductive fluids the equations of motion of compressible viscous and heat conductive fluids are investigated for initial boundary value problems on the half space and on the exterior domain of any bounded region the global solution in time is proved to exist uniquely and approach the stationary state ast provided the prescribed initial data and the external force are sufficiently small

large time behavior of solutions to the compressible navier stokes equations around periodic steady states abstract this paper shows that the strong solution to the compressible navier stokes equation around spatially periodic stationary solution in a periodic layer of r n n 2 3 exists globally in time if reynolds and mach numbers are sufficiently small it is proved that the asymptotic leading part of the perturbation is given by a solution to the one dimensional viscous burgers equation multiplied by a spatially periodic function when n 2 and by a solution to the two dimensional heat equation multiplied by a spatially periodic function when n 3

interior a priori estimates for solutions of fully non linear equations on etend une theorie de perturbations aux solutions d equations uniformement elliptiques d ordre 2 totalement non lineaires

the l p dirichlet problem and nondivergence harmonic measure we consider the dirichlet problem lu 0 in d u g on d for two second order elliptic operators l k u n i j 1 a i j k x ij u x k 0 1 in a bounded lipschitz domain d r n the coefficients a i j k belong to the space of bounded mean oscillation bmo with a suitable small bmo modulus we assume that l 0 is regular in l p d d for some p 1 p that is nu lp c g lp for all continuous boundary data g here is the surface measure on d and nu is the nontangential maximal operator the aim of this paper is to establish sufficient conditions on the difference of the coefficients e i j x a i j 1 x a i j 0 x that will assure the perturbed operator l 1 to be regular in l q d d for some q 1 q

boundary regularity in variational problems we prove that if u omega subset mathbb r n to mathbb r n is a solution to the dirichlet variational problem mathop rm min limits w int omega f x w dw rm d x quad rm subject to quad w equiv u 0 rm on partial omega involving a regular boundary datum u 0 and a regular integrand f x w dw strongly convex in dw and satisfying suitable growth conditions then mathcal h n 1 almost every boundary point is regular for u in the sense that du is holder continuous in a relative neighborhood of the point the existence of even one such regular boundary point was previously not known except for some very special cases treated by jost meier math ann 262 549 561 1983 our results are consequences of new up to the boundary higher differentiability results that we establish for minima of the functionals in question the methods also allow us to improve the known boundary regularity results for solutions to non linear elliptic systems and in some cases to improve the known interior singular sets estimates for minimizers moreover our approach allows for a treatment of systems and functionals with rough coefficients belonging to suitable sobolev spaces of fractional order

large time behavior of the semigroup on lp spaces associated with the linearized compressible navier stokes equation in a cylindrical domain abstract large time behavior of solutions to the linearized compressible navier stokes equation around the motionless state in a cylindrical domain is investigated the l p decay estimates of the associated semigroup are established for all 1 p it is also shown that the time asymptotic leading part of the semigroup is given by a one dimensional heat semigroup