On the solutions of a model equation for shallow water waves of moderate amplitude

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:255

Article

Mi, Yongsheng^1,2  Mu, Chunlai¹ 

[1] Chongqing Univ, Coll Math & Stat, Chongqing 401331, Peoples R China

[2] Yangtze Normal Univ, Coll Math & Comp Sci, Chongqing 408100, Peoples R China

关键词: Besov spaces;    Camassa-Holm equation;    Local well-posedness;   

DOI  :  10.1016/j.jde.2013.06.008

来源: Elsevier

【 摘 要 】

This paper is concerned with the Cauchy problem of a model equation for shallow water waves of moderate amplitude, which was proposed by A. Constantin and D. Lannes [The hydrodynamical relevance of the Camassa-Holmand Degasperis-Procesi equations, Arch. Ration. Mech. Anal. 192 (2009) 165-186]. First, the local well-posedness of the model equation is obtained in Besov spaces B-p,r(s), p, r is an element of [1, infinity], s > max{3/2, 1 + 1/p} (which generalize the Sobolev spaces H-s) by using Littlewood-Paley decomposition and transport equation theory. Second, the local well-posedness in critical case (with s = 3/2, p = 2, r = 1) is considered. Moreover, with analytic initial data, we show that its solutions are analytic in both variables, globally in space and locally in time. Finally, persistence properties on strong solutions are also investigated. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free