Wave breaking and global existence for a family of peakon equations with high order nonlinearity. (February 2019)

• Record Type: Journal Article
• Authors: Yan, Kai
• Is Part Of: Nonlinear analysis. Volume 45(2019)
• Page Start: 721
• Page End: 735
• Publication Date: 2019-02
• Subjects: Wave breaking -- Global existence -- Blow-up -- Peakons -- Shallow water wave equations -- High order nonlinearity; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2018.07.032
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: This paper is concerned with the Cauchy problem for a family of peakon equations with high order nonlinearity. To begin with, the local well-posedness results in Besov and Sobolev spaces are discussed. Then we obtain the precise blow-up scenario for strong solutions to the equation, which is conjectured by Anco et al., (2015). Moreover, we establish some global existence results for the strong solutions by deriving two useful conservation laws. Furthermore, wave breaking phenomenon is studied and we construct a new finite time blow-up solution to the equation with respect to the initial data.