The Cauchy problem of a weakly dissipative shallow water equation. Issue 8 (11th June 2019)

• Record Type: Journal Article
• Authors: Ming, Sen; Lai, Shaoyong; Su, Yeqin
• Is Part Of: Applicable analysis. Volume 98:Issue 8(2019)
• Page Start: 1387
• Page End: 1402
• Publication Date: 2019-06-11
• Subjects: Local well-posedness -- weakly dissipative shallow water equation -- blow-up -- global solution; 35G25 -- 35L15; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2017.1422728
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: The local well-posedness for the Cauchy problem of a weakly dissipative shallow water equation is established using the Littlewood–Paley theory and a priori estimates of solutions to the transport equation. The H 1 ( R ) norm estimates, the blow-up mechanisms, and the global existence of solutions to the problem are investigated. The novelty is that the effects of the weakly dissipative coefficients and nonlinear index to guarantee the global existence of solutions are presented.