摘要
该文研究七阶非线性弱色散方程:ut+au xu+βx3u3+γx5u5+μx7u7=0,(x,t)∈R2的初值问题,通过运用震荡积分衰减估计的最近结果,首先对相应线性方程的基本解建立了几类Strichartz型估计.其次,应用这些估计证明了七阶非线性弱色散方程初值问题解的局部与整体存在性和唯一性.结果表明,当初值u0(x)∈Hs(R),s≥2/13时,存在局部解;当s≥1时,存在整体解.
This paper is devoted to studying the initial value problem of a class of seventh order weakly nonlinear dispersive equations δu/δt+au δu/δx+β δ^3u/δx^3 +γδ^5u/δx^5 +μ δ^7u/δx^7=0, (x,t)∈R^2, By using recently established decay estimates for oscillatory integrals, the authors first establish several Strichartz type estimates for the fundamental solution of the corresponding linear problem. Then the authors prove that a local solution exists if the initial function u0(x)∈H^5(R),s≥2/13 ,and a global solution exists if s≥1.
出处
《数学物理学报(A辑)》
CSCD
北大核心
2005年第4期451-460,共10页
Acta Mathematica Scientia
基金
国家自然科学基金(10271095)
NWNU-KJCXGC-212基金资助
关键词
色散方程
初值问题
解
局部存在性
整体存在性.
Dispersive equation
Initial value problem
Solution
Local existence
Global existence.