Low Regularity Well-Posedness for Nonlinear Wave Equations
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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.Abstract: Low regularity well-posedness for the Cauchy problem of some nonlinear wave equations was studied.The Cauchy problem is well posed when the Sobolev exponents for the initial data is higher than a critical value.Otherwise,it is ill posed.The known results were extened from n=3 to n=1.The method in provement is based on energy estimate,scaling transform,and selection of initial values.
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Key words:
- nonlinear wave equation /
- low regularity /
- well-posedness /
- ill-posedness /
- Sobolev exponents
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