Non-uniform continuity in $H\sp 1$ of the solution map of the CH equation
Non-uniform continuity in $H\sp 1$ of the solution map of the CH equation
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DOI：
10.4310/ajm.2007.v11.n1.a13
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发表时间：
2007-03
影响因子：
0.6
通讯作者：
A. Himonas;G. Misiołek;G. Ponce
中科院分区：
文献类型：
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作者：
A. Himonas;G. Misiołek;G. Ponce
证明了Camassa-Holm方程的解映射在环面和真实的直线上的一阶Sobolev空间中对初值不是一致连续的.证明依赖于非光滑行波解的建设。我们还扩展到所有的Hs的早期结果已知持有峰。
We show that the solution map of the Camassa-Holm equation is not uniformly continuous in the initial data in the Sobolev space of order one on the torus and the real line. The proof relies on a construction of non-smooth travelling wave solutions. We also extend to all Hs an earlier result known to hold for peakons.