Global Existence of Solutions for the Cauchy Problem of the Kawahara Equation with L 2 Initial Data期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Global Existence of Solutions for the Cauchy Problem of the Kawahara Equation with L 2 Initial Data

Authors:	Shang Bin Cui Dong Gao Deng Shuang Ping Tao

Affiliation:	(1) Department of Mathematics, Sun Yat-Sen University, Guangzhou 510275, P. R. China;(2) Department of Mathematics, Northwest Normal University, Lanzhou 730070, P. R. China

Abstract:	In this paper we study solvability of the Cauchy problem of the Kawahara equation $partial _{t} u + aupartial _{x} u + beta partial ^{3}_{x} u + gamma partial ^{5}_{x} u = 0$ with L ² initial data. By working on the Bourgain space X ^r,s(R ²) associated with this equation, we prove that the Cauchy problem of the Kawahara equation is locally solvable if initial data belong to H ^r(R) and −1 < r ≤ 0. This result combined with the energy conservation law of the Kawahara equation yields that global solutions exist if initial data belong to L ²(R). Project supported by the China National Natural Science Foundation (Grants 10171111, 10171112)

Keywords:	Kawahara equation Cauchy problem global solution
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