The Cauchy problem for a generalized Camassa–Holm equation with the velocity potential. Issue 3 (17th February 2018)

• Record Type: Journal Article
• Authors: Lin, Bohuan; Yin, Zhaoyang
• Is Part Of: Applicable analysis. Volume 97:Issue 3(2018)
• Page Start: 354
• Page End: 367
• Publication Date: 2018-02-17
• Subjects: A generalized Camassa–Holm equation with the velocity potential -- local well-posedness -- blow-up -- cuspon weak solutions; 35G25 -- 35L05; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2016.1267342
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract: In this paper, we discuss a generalized Camassa–Holm equation whose solutions are velocity potentials of the classical Camassa–Holm equation. By exploiting the connection between these two equations, we first establish the local well-posedness of the new equation in the Besov spaces and deduce several blow-up criteria and blow-up results. Then, we investigate the existence of global strong solutions and present a class of cuspon weak solutions for the new equation.