Search

Abstract: The Landau equation describes the binary collisional effects (through long range coulombian interaction) in a plasma. In this paper, we prove that the known classical solutions to the Landau equation near Maxwellian in the whole space have a regularizing effect in all (time, space and velocity) variables, that is, become immediately smooth with respect to all variables. [Copyright &y& Elsevier]

Abstract: The Cauchy problem of the Landau equation with potential forces on torus is investigated. The global existence of solutions with the symmetry of origin and the exponential convergence rate in time to the steady state are obtained for any initially smooth, periodic, origin symmetric small perturbation. [Copyright &y& Elsevier]

Abstract: This paper is concerned with the optimal temporal decay estimates on the solutions of the Cauchy problem of the Cahn–Hilliard equation. It is shown in Liu, Wang and Zhao (2007) that such a Cauchy problem admits a unique global smooth solution provided that the smooth nonlinear function satisfies a local growth condition. Furthermore if satisfies a somewhat stronger local growth condition, the optimal temporal decay estimates on are also obtained in Liu, Wang and Zhao (2007) . Thus a natural question is how to deduce the optimal temporal decay estimates on only under the local growth condition which is sufficient to guarantee the global solvability of the corresponding Cauchy problem and the main purpose of this paper is devoted to this problem. Our analysis is motivated by the technique developed recently in Ukai, Yang and Zhao (2006) with a slight modification. [ABSTRACT FROM AUTHOR]

Abstract: This paper is devoted to the following rescaled Boltzmann equation in the acoustic time scaling in the whole space with prescribed initial data For a solution to the rescaled Boltzmann equation (0.1) in the whole space for all with initial data our main purpose is to justify the global-in-time uniform energy estimates of in ϵ and prove that converges strongly to whose dynamic is governed by the acoustic system. [Copyright &y& Elsevier]