Improved Local Wellposedness of Cauchy Problem for Generalized KdV-BO Equation  

作　　者：ZHAO Xiang Qing GUO Ai 

机构地区：[1]Department of Mathematics, Zhejiang Ocean University, Zhejiang 316000, China [2]School of Mathematical Sciences, South China University of Technology, Guangdong 510640, China

出　　处：《Journal of Mathematical Research and Exposition》2009年第2期371-375,共5页数学研究与评论（英文版）

基　　金：the Natural Science Foundation of Zhejiang Province （No. Y6080388）; the Science and Technology Research Foundation of Zhejiang Ocean University （Nos. X08M014; X08Z04）.

摘　　要：In this paper we prove that the Cauchy problem associated with the generalized KdV-BO equation ut ＋ uxxx ＋ λH（uxx） ＋ u^2ux = 0, x ∈ R, t ≥ 0 is locally wellposed in Hr^s（R） for 4/3 〈r≤2, b〉1/r and s≥s（r）= 1/2- 1/2r. In particular, for r = 2, we reobtain the result in [3].In this paper we prove that the Cauchy problem associated with the generalized KdV-BO equation ut + uxxx + λH(uxx) + u2ux = 0, x ∈ R, t ≥ 0 is locally wellposed in Hrs(R) for 34 < r ≤ 2, b > r1 and s ≥ s(r) = 21 21r. In particular, for r = 2, we reobtain the result in [3].

关 键 词：KdV-BO equation Cauchy problem local wellposedness. 

分 类 号：O175.2[理学—数学]