| 高阶色散方程的柯西问题 |
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| 作者单位： | ;1.河南师范大学数学与信息科学学院 |
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| 摘 要： | 主要研究了高阶色散方程ut+2j+1xu=j+1x(u2)+j-1x(ux2),j≥2,j∈N,x,t∈R的柯西问题.使用修正傅里叶限制范数方法和Strichartz估计以及修正Bourgain空间,证明了这个问题在修正的Sobolev空间H(s,1/2j)(s-j/2+3/4)上是局部适定的.使用迭代技巧,也证明了这个问题在H(s,w)(0w1/2j)中,对于任意的s∈R,流映射不是C2的.
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| 关 键 词： | 柯西问题 局部适定 修正的Sobolev空间 |
The Cauchy Problem for the Higher-Order Dispersive Equation |
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| Institution: | ,College of Mathematics and Information Science,Henan Normal University |
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| Abstract: | In this paper,we consider the Cauchy problem for the higher-order dispersive equation ut+2j+1xu=j+1x(u2)+j-1x(u2x),j≥2,j∈N,x,t∈R.By using the modified Fourier restriction norm method and Strichartz estimate and the modified Bourgain space,we prove that the problem is locally well-posed in modified Sobolev space H(s,1/2j) with s>-j/2+3/4.By using the iteration technique,we also prove that the flow map is not C2 at the origin if we assume that the problem is well-posed in H(s,w)with 0
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| Keywords: | Cauchy problem local well-posedness modified Sobolev spaces |
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