Well‐posedness for the Cauchy problem of the modified Hunter–Saxton equation in the Besov spaces. (19th December 2014)

• Record Type: Journal Article
• Authors: Mi, Yongsheng; Mu, Chunlai
• Is Part Of: Mathematical methods in the applied sciences. Volume 38:Number 17(2015:Nov. 30)
• Page Start: 4061
• Page End: 4074
• Publication Date: 2014-12-19
• Subjects: Besov spaces -- Camassa–Holm type equation -- local well‐posedness -- subclass35B30 -- 35G25 -- 35A10 -- 35Q53; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.3346
• Languages: English
• ISSNs: 0170-4214

Abstract

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 B p, r s, p, r ∈ [ 1, ∞ ], s > max 3 2, 1 + 1 p (which generalize the Sobolev spaces H s ) by using Littlewood‐Paley decomposition and transport equation theory. Moreover, the local well‐posedness in critical case (with s = 3 2, p = 2, r = 1 ) is considered.