On Cauchy Problem of the Benney-Lin Equation with Low Regularity Initial Data  

作　　者：Xiang Qing ZHAO Shang Bin CUI 

机构地区：[1]Department of Mathematics, Zhejiang Ocean University, Zhoushan 316000, P. R. China [2]Department of Mathematics, Shanghai University, Shanghai 200444, P. R. China [3]Institute of Mathematics, Sun Yat-Sen University, Guangzhou 510275, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2009年第12期2157-2168,共12页数学学报（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant No.10771223)

摘　　要：In this work we prove that the initial value problem of the Benney-Lin equation ut ＋ uxxx ＋ β（uxx ＋ u xxxx） ＋ ηuxxxxx ＋ uux = 0 （x ∈ R, t ≥0 0）, where β 〉 0 and η∈R, is locally well-posed in Sobolev spaces HS（R） for s ≥ -7/5. The method we use to prove this result is the bilinear estimate method initiated by Bourgain.In this work we prove that the initial value problem of the Benney-Lin equation ut ＋ uxxx ＋ β（uxx ＋ u xxxx） ＋ ηuxxxxx ＋ uux = 0 （x ∈ R, t ≥0 0）, where β 〉 0 and η∈R, is locally well-posed in Sobolev spaces HS（R） for s ≥ -7/5. The method we use to prove this result is the bilinear estimate method initiated by Bourgain.

关 键 词：Benney-Lin equation initial value problem local well-posedness 

分 类 号：O175.27[理学—数学] G633.6[理学—基础数学]