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Well‐posedness for the Cauchy problem of the modified Hunter–Saxton equation in the Besov spaces |
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| Authors: | Yongsheng Mi Chunlai Mu |
| Affiliation: | 1. Institute of Applied Physics and Computational Mathematics, Beijing 100088, PR China;2. College of Mathematics and Computer Sciences, Yangtze Normal University, Fuling 408100, Chongqing, PR China;3. College of Mathematics and Statistics, Chongqing University, Chongqing 401331, PR China |
| Abstract: | This paper is concerned with the Cauchy problem of the modified Hunter‐Saxton equation. The local well‐posedness of the model equation is obtained in Besov spaces  (which generalize the Sobolev spaces Hs) by using Littlewood‐Paley decomposition and transport equation theory. Moreover, the local well‐posedness in critical case (with  ) is considered. |
| Keywords: | Besov spaces Camassa– Holm type equation local well‐posedness subclass35B30 35G25 35A10 35Q53 |