Well-posedness and analyticity for the Cauchy problem for the generalized Camassa–Holm equation
Well-posedness and analyticity for the Cauchy problem for the generalized Camassa–Holm equation
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DOI：
10.1016/j.jmaa.2013.03.020
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发表时间：
2013-09
影响因子：
1.3
通讯作者：
Yongsheng Mi;Chunlai Mu
中科院分区：
文献类型：
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作者：
Yongsheng Mi;Chunlai Mu
本文研究了Hakkaev和Kirchev [S.哈卡耶夫河Kirchev，Local well-posedness and orbital stability of solid wave solutions for the generalized Camassa-Holm equation，Comm. Partial Differential Equations 30（2005）761-781].我们建立了一系列Besov空间的局部适定性。在解析初值条件下，证明了该方程的解在空间上是整体解析的，在时间上是局部解析的，推广了Danchin [R. Danchin，A few remarks on the Camassa-Holm equation，Differential Integral Equations 14（2001）953-988] and Himonas and Misiolek [A.希莫纳斯湾Misiolek，Analyticity of the Cauchy problem for an integrable evolution equation，Math.Ann.327（2003）575-584]到更一般的方程。
In this paper, we are concerned with the Cauchy problem for the generalized Camassa–Holm equation, which was proposed by Hakkaev and Kirchev [S. Hakkaev, K. Kirchev, Local well-posedness and orbital stability of solitary wave solutions for the generalized Camassa–Holm equation, Comm. Partial Differential Equations 30 (2005) 761–781]. We establish the local well-posedness for a range of Besov spaces. Moreover, with analytic initial data, we show that its solutions are analytic in both variables, globally in space and locally in time, which extends some results of Danchin [R. Danchin, A few remarks on the Camassa–Holm equation, Differential Integral Equations 14 (2001) 953–988] and Himonas and Misiolek [A. Himonas, G. Misiolek, Analyticity of the Cauchy problem for an integrable evolution equation, Math. Ann. 327 (2003) 575–584] to more general equations.