Global Well-posedness of the Stochastic Generalized Kuramoto-Sivashinsky Equation with Multiplicative Noise  

作　　者：Wei WU Shang-bin CUI Jin-qiao DUAN 

机构地区：[1]Science and Information College, Qingdao Agricultural University, Qingdao 266109, China [2]Department of Mathematics, Sun Yat-Sen University, Guangzhou 510275, China [3]Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL 60616, USA [4]Center for Mathematical Sciences, Huazhong University of Science and Technology, Wuhan 430074, China

出　　处：《Acta Mathematicae Applicatae Sinica》2018年第3期566-584,共19页应用数学学报（英文版）

基　　金：Supported by the National Natural Science Foundation of China(No.11571381,11531006,11771449);the National Science Foundation(No.1620449);the High Level Talent Foundation of Qingdao Agricultural University(No.663-1113305)

摘　　要：Global well-posedness of the initial-boundary value problem for the stochastic generalized KuramotoSivashinsky equation in a bounded domain D with a multiplicative noise is studied. It is shown that under suitable sufficient conditions, for any initial data u0 ∈L2（D×Ω）, this problem has a unique global solution u in the space L2（Ω, C（[0, T ], L2（D））） for any T 〉 0, and the solution map u0 →u is Lipschitz continuous.Global well-posedness of the initial-boundary value problem for the stochastic generalized KuramotoSivashinsky equation in a bounded domain D with a multiplicative noise is studied. It is shown that under suitable sufficient conditions, for any initial data u0 ∈L2（D×Ω）, this problem has a unique global solution u in the space L2（Ω, C（[0, T ], L2（D））） for any T 〉 0, and the solution map u0 →u is Lipschitz continuous.

关 键 词：Kuramoto-Sivashinsky equation stochastic partial differential equations multiplicative noise well-posedness 

分 类 号：O175[理学—数学]