Asymptotic Smoothing Effect of Solutions to Davey-Stewartson Systems on the Whole Plane  

作　　者：Cai Di ZHAO Yong Sheng LI Sheng Fan ZHOU 

机构地区：[1]School of Mathematics and Information Science, Wenzhou University, Wenzhou 325035, P. R. China [2]Department of Mathematical Sciences,South China University of Technology, Guangdong, 510640, P. R. China [3]Department of Applied Mathematics, Shanghai Normal University, Shanghai 200234, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2007年第11期2043-2060,共18页数学学报（英文版）

基　　金：Natural Science Foundation of China under grant numbers 10471047 and 10471086;Zhejiang Province Natural Science Foundation with item M103043;Natural Science Foundation of Guangdong Province of China under grant No.004020077

摘　　要：This paper discusses the Cauchy problem of elliptic-elliptic-type Davey-Stewartson systems with zero-order dissipation on R^2. Making use of the Fourier spectral projector, together with a long time comparison between the solutions to the Davey-Stewartson systems and to an auxiliary problem, we prove that the global attractor in H^1 （R^2） for the addressed Davey-Stewartson systems is a compact subset of H^2（R^2）, and thus reveal the asymptotic smoothing effect of the solutions for the systems.This paper discusses the Cauchy problem of elliptic-elliptic-type Davey-Stewartson systems with zero-order dissipation on R^2. Making use of the Fourier spectral projector, together with a long time comparison between the solutions to the Davey-Stewartson systems and to an auxiliary problem, we prove that the global attractor in H^1 （R^2） for the addressed Davey-Stewartson systems is a compact subset of H^2（R^2）, and thus reveal the asymptotic smoothing effect of the solutions for the systems.

关 键 词：Davey-Stewartson systems asymptotic smoothing effect global attractor zero-order dissipation 

分 类 号：O175.2[理学—数学]