In this paper,we study a nematic liquid crystals system in three-dimensional whole space R^3 and obtain the time decay rates of the higher-order spatial derivatives of the solution by the method of spectral analysis and energy estimates if the initial data belongs to L^1(R^3) additionally.
The incompressible limit of the non-isentropic magnetohydrodynamic equations with zero thermal coefficient,in a two dimensional bounded domain with the Dirichlet condition for velocity and perfectly conducting boundary condition for magnetic field,is rigorously justified.
In this paper,the infinite Prandtl number limit of Rayleigh-B′enard convection is studied.For well prepared initial data,the convergence of solutions in L∞(0,t;H2(G)) is rigorously justified by analysis of asymptotic expansions.
We give three equivalent conditions for non-accessibility of an Anosov diffeomorphism on the 3-torus with a partially hyperbolic splitting. Since accessibility is an open property, this gives a negative answer to Hammerlindl's question about homology boundedness of strong unstable foliation.
This paper deals with the problem of sharp observability inequality for the 1-D plate equation wtt + wxxxx + q(t,x)w = 0 with two types of boundary conditions w = wxx = 0 or w = wx = 0,and q(t,x) being a suitable potential.The author shows that the sharp observability constant is of order exp(C q ∞27) for q ∞≥ 1.The main tools to derive the desired observability inequalities are the global Carleman inequalities,based on a new point wise inequality for the fourth order plate operator.
We investigate the ratio of L 1 and L 2 norms of the Cauchy problem solutions of heat equations with compact support initial data.The related asymptotic behavior of the eigenvalues and eigenfunctions of certain integral operators is obtained.
DING YuTao 1,2,& ZHANG LiQun 1,2 1 Institute of Mathematics,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China
In this article, we study the existence of nontrivial solutions for a class of asymptotically linear Hamiltonian systems with Lagrangian boundary conditions by the Galerkin approximation methods and the L-index theory developed by the first author.
