global regular and singular solutions for a model of gravitating particles the existence of solutions of a nonlinear parabolic equation describing the gravitational interaction of particles is studied for the initial data in spaces of generalized pseudomeasures this approach permits us to relax regularity assumptions on the initial conditions and to prove asymptotic stability results for the above problem

the drift diffusion system in two dimensional critical hardy space abstract we establish the time local well posedness for large data of a solution to two dimensional drift diffusion system in the critical hardy space h 1 r 2 this solution is obtained in the hardy class for which the natural free energy is well defined from the initial time the time global well posedness result for small data is also obtained in a similar class the crucial parts of the proof are to employ the end point type of maximal regularity for the homogeneous heat equation and some new bilinear estimates in the hardy space

discrete subgroups of mobius transformations abstract in this paper we present the necessary geometric conditions for a nonelementary two generator subgroup of mobius transformations acting in r n r n to be discrete

on the well posedness of the euler equations in the triebel lizorkin spaces we prove local in time unique existence and a blowup criterion for solutions in the triebel lizorkin space for the euler equations of inviscid incompressible fluid flows in n n 2 as a corollary we obtain global persistence of the initial regularity characterized by the triebel lizorkin spaces for the solutions of two dimensional euler equations to prove the results we establish the logarithmic inequality of the beale kato majda type the moser type of inequality as well as the commutator estimate in the triebel lizorkin spaces the key methods of proof used are the littlewood paley decomposition and the paradifferential calculus by j m bony 2002 john wiley sons inc

on a theorem of benson and curtis iwahori conjectured 5 that the hecke algebra over q of a chevalley group g over a finite field f with respect to a bore1 subgroup is isomorphic to the group algebra over q of the weyl group the analogous statement with q replaced by its algebraic closure was proved by tits 3 ex 27 p 561 using a deformation argument in 11 benson and curtis proved using a case by case analysis that iwahori s conjecture is true over q whenever g is simple of type ze e with the help of springer they proved that when g is of type e or e there exists irreducible representations of the hecke algebra whose character involve 4 and hence iwahori s conjecture over q is false in general the main result of this paper is an explicit construction of an isomorphism of the hecke algebra over q q with the group algebra over q q of the weyl group the construction makes essential use of the polynomials p w of 8 at some point in the proof i have to appeal to the interpretation of p l in terms of multiplicities in verma modules 8 i 51 which has recently been established by brylinski and kashiwara 4 and independently by belinson and bernstein

optimal l p l q estimates for parabolic boundary value problems with inhomogeneous data in this paper we investigate vector valued parabolic initial boundary value problems mathcal a t x d mathcal b j t x d subject to general boundary conditions in domains g in mathbb r n with compact c 2m boundary the top order coefficients of mathcal a are assumed to be continuous we characterize optimal l p l q regularity for the solution of such problems in terms of the data we also prove that the normal ellipticity condition on mathcal a and the lopatinskii shapiro condition on mathcal a mathcal b 1 dots mathcal b m are necessary for these l p l q estimates as a byproduct of the techniques being introduced we obtain new trace and extension results for sobolev spaces of mixed order and a characterization of triebel lizorkin spaces by boundary data

cells and the reflection representation of weyl groups and hecke algebras let f be the generic algebra of the finite crystallographic coxeter group w defined over the ring q u1 2 u 2 first the two sided cell corresponding to the reflection representation of f is shown to consist of the nonidentity elements of w having a unique reduced expression next the matrix entries of this representation are computed in terms of certain kazhdanlusztig polynomials finally the kazhdan lusztig polynomials just mentioned are described in case w is of type a1 lor b

reflection representations of hecke algebras of certain weyl groups soit w un groupe de weyl et soit s l ensemble correspondant des reflexions simples soit h l algebre de hecke on donne des proprietes de la representation reflexion de l algebre de hecke h w

simple transitive 2 representations of small quotients of soergel bimodules in all finite coxeter types but i2 12 i2 18 and i2 30 we classify simple transitive 2 representations for the quotient of the 2 category of soergel bimodules over the coinvariant algebra which

kazhdan lusztig polynomials for hermitian symmetric spaces on presente un schema non recursif pour calculer le polynome de kazhdan lusztig associe a un espace hermitien symetrique classique on donne un tableau des polynomes pour les domaines hermitiens exceptionnels

end point maximal regularity and its application to two dimensional keller segel system we prove the maximal l regularity of the cauchy problem of the heat equation in the besov space dot b 1 rho 0 mathbb r n 1 which is not umd space and as its application we establish the time local well posedness of the solution of two dimensional nonlinear parabolic system with the poisson equation in dot b 1 2 0 mathbb r 2 where the equation is considered in the space invariant by a scaling and particularly the natural free energy is well defined from the initial time the small data global existence is also obtained in the same class

large time behavior of the vorticity of two dimensional viscous flow and its application to vortex formation we consider the cauchy problem for the two dimensional vorticity equation we show that the solution behaves like a constant multiple of the gauss kernel having the same total vorticity as time tends to infinity no particular structure of initial data 0 x 0 is assumed except the restriction that the reynolds numberr 0 dx v is small wherev is the kinematic viscosity applying a time dependent scale transformation we show a stability of burgers vortex which physically implies formation of a concentrated vortex

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

smooth or singular solutions to the navier stokes system abstract the existence of singular solutions of the incompressible navier stokes system with singular external forces the existence of regular solutions for more regular forces as well as the asymptotic stability of small solutions including stationary ones and a pointwise loss of smoothness for solutions are proved in the same function space of pseudomeasure type

weak solutions to a parabolic elliptic system of chemotaxis abstract we study a parabolic elliptic system of partial differential equations which describes the chemotactic feature of slime molds it is known that the blowup solution forms singularities such as delta functions referred to as the collapses here we study the case that the domain is a flat torus and show that the post blowup continuation of the solution is possible only when those collapses are quantized with the mass 8

largest well posed spaces for the general diffusion system with nonlocal interactions abstract the authors derive a general diffusion gd system with nonlocal interactions of special structure via energetic variational approach and observe that there exist two critical values of s i e s 1 2 1 for the nonlocal interactions where s 1 2 reflects how strong nonlocal property we have and s 1 affects the linearization and choice of initial data spaces the authors also establish the global existence and uniqueness of mild solution

the navier stokes equations in the weak l n space with time dependent external force abstract we consider the navier stokes equations with time dependent external force either in the whole time or in positive time with initial data with domain either the whole space the half space or an exterior domain of dimension n ge 3 we give conditions on the external force sufficient for the unique existence of small solutions in the weak l n space bounded for all time in particular this result gives sufficient conditions for the unique existence and the stability of small time periodic solutions or almost periodic solutions this result generalizes the previous result on the unique existence and the stability of small stationary solutions in the weak l n space with time independent external force

singularity patterns in a chemotaxis model the authors study a chemotactic model under certain assumptions and obtain the existence of a class of solutions which blow up at the center of an open disc in finite time such a finite time blow up of solutions implies chemotactic collapse namely concentration of species to form sporae the model studied is the limiting case of a basic chemotactic model when diffusion of the chemical approaches infinity which has the form ut u u v 0 v u 1 on r2 where is an open disc with no flux homogeneous neumann boundary conditions the initial conditions are continuous functions u x 0 u0 x 0 v x 0 v0 x 0 for x under these conditions the authors prove there exists a radially symmetric solution u r t which blows up at r 0 t t a specific description of such a solution is presented the authors also discuss the strong similarity between the chemotactic model they study and the classical stefan problem

well posedness for the drift diffusion system in lp arising from the semiconductor device simulation abstract we discuss strong solutions of a nonlinear parabolic system that arise from the simulation for the semiconductor device design this equation considered here is governing the electron and positive hole dynamics on the mos fet for the large scaled integral circuit v lsi we show that the existence and uniqueness and stability of the strong solution in l p spaces and will discuss on the global existence

gevrey regularity of mild solutions to the parabolic elliptic system of drift diffusion type in critical besov spaces abstract this paper is devoted to studying analyticity of mild solutions to the parabolic elliptic system of drift diffusion type with small initial data in critical besov spaces more precisely by using multilinear singular integrals and fourier localization argument we show that global in time mild solutions are gevrey regular i e e t 1 v e t 1 w l t b p r 2 n p r n l t 1 b p r n p r n for all 1 p 2 n and 1 r where 1 is the fourier multiplier whose symbol is given by 1 i 1 n i as a corollary we obtain decay estimates of mild solutions in critical besov spaces without using cumbersome recursive estimation of higher order derivatives

asymptotic expansion of solutions to the drift diffusion equation with fractional dissipation abstract the initial value problem for the drift diffusion equation arising from the model of semiconductor device simulations is studied the dissipation on this equation is given by the fractional laplacian 2 large time behavior of solutions to the drift diffusion equation with 0 1 is discussed when 1 large time behavior of solutions is known however when 0 1 the perturbation methods used in the preceding works would not work in this paper the asymptotic expansion of solutions with high order is derived