七阶非线性色散方程初值问题解的局部和整体存在性

Abstract

Abstract:

This paper is devoted to studying the initial value problem of a class of seventh order weakly nonlinear dispersive equations:∂u/∂t + au(∂u/∂x) +β(∂^3 u /∂x^3) +γ(∂^5 u/∂x^5) + μ(∂^7 u/∂x^7)=0, (x,t)∈R^2.By using recently established decay estimates for oscillatory integrals, the authors firs t establish several Strichartz type estimates for the fundamental solution of the corresponding linear problem. Then the authors prove that a local solution exists if t he initial function u_0(x)∈H^s(R), s≥2/13, and a global solution exists if s≥1.

Key words: Dispersive equation, Initial value problem; , Solution; , Local existence, Global existence

CLC Number:

35Q30

DAO Shuang-Beng, CUI Chang-Bin. The Initial Value Problem of the Seventh Order Weakly Dispersi ve Equations[J].Acta mathematica scientia,Series A, 2005, 25(4): 451-460.

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The Initial Value Problem of the Seventh Order Weakly Dispersi ve Equations

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