一类弱耗散Camassa-Holm方程局部强解的适定性及弱解的存在性  

Local well-posedness and weak solutions for a weakly dissipative Camassa-Holm equation

作　　者：赖绍永[1] 吴永洪 

机构地区：[1]西南财经大学应用数学系,成都610074 [2]Department of Mathematics and Statistics,Curtin University of Technology

出　　处：《中国科学：数学》2010年第9期901-920,共20页Scientia Sinica：Mathematica

基　　金：教育部科学技术研究重点项目(批准号:109140)资助

摘　　要：使用Pseudoparabolic正则化方法和从弱耗散Camassa-Holm方程自身导出的估计式,在Sobolev空间Hs(R)(s>3/2)中,证明了该Camassa-Holm方程解的局部适定性.同时给出了一个在空间Hs(R)(1<s2\3)中确保该方程弱解存在的充分条件.The local well-posedness of solutions for a weakly dissipative Camassa-Holm equation in the Sobolev space Hs （R） with s 〉 3 is established by using the pseudoparabolic regularization technique and some estimates derived from the equation itself. A sufficient condition which guarantees the existence of weak solutions for the equation in lower order Sobolev space Hs with 1〈s≤3/2 is developed.

关 键 词：局部适定性 耗散Camassa-Holm方程 高阶非线性项 弱解 

分 类 号：O175.29[理学—数学]