非线性波动方程的低正则适定性  

Low Regularity Well-Posedness for Nonlinear Wave Equations

作　　者：杨晗[1] 毋海根[1] 

机构地区：[1]西南交通大学应用数学系,四川成都610031

出　　处：《西南交通大学学报》2006年第1期127-130,共4页Journal of Southwest Jiaotong University

基　　金：国家自然科学基金资助项目(10301026);国家杰出青年基金资助项目(10225102)

摘　　要：研究一类非线性波动方程的柯西问题的低正则适定性.证明了当初值的Sobolev正则性高于一临界值时,柯西问题是适定的,否则其是不适定的.将空间维数n=3的已有结果推广到空间维数n=1.证明方法是基于能量估计和尺规变换,并选择适当的初值.Low regularity well-posedness for the Cauchy problem of some nonlinear wave equations was studied. The Cauchy problem is well than a critical value. Otherwise, it is The method in provement is based values. posed when the Soholev exponents for the initial data is higher ill posed. The known results were extened from n = 3 to n = 1. on energy estimate, scaling transform, and selection of initial

关 键 词：非线性波动方程 低正则 适定性 不适定性 SOBOLEV指数 

分 类 号：O175.29[理学—数学] O175.25[理学—基础数学]