Local and Global Existence of Solutions toInitial Value Problems of Modified NonlinearKawahara Equations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

Local and Global Existence of Solutions toInitial Value Problems of Modified NonlinearKawahara Equations

Authors:	Shuang Ping Tao Shang Bin Cui

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

Abstract:	This paper is devoted to studying the initial value problem of the modified nonlinear Kawahara equation $frac{{partial u}} {{partial t}} + afrac{{u^{2} partial u}} {{partial x}} + beta frac{{partial ^{3} u}} {{partial x^{3} }} + gamma frac{{partial ^{5} u}} {{partial x^{5} }} = 0,$ (x,t) ∈ R ². We first establish several Strichartz type estimates for the fundamental solution of the corresponding linear problem. Then we apply such estimates to prove local and global existence of solutions for the initial value problem of the modified nonlinear Karahara equation. The results show that a local solution exists if the initial function u ₀(x) ∈ H ^s(R) with s ≥ 1/4, and a global solution exists if s ≥ 2. Supported by NWNU-KJCXGC-212 and NWNU-QNJSJJ

Keywords:	Kawahara equation Initial value problem Solution Local existence Global existence
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