The Cauchy problem for a generalized Camassa–Holm equation with the velocity potential

Bohuan Lin, Zhaoyang Yin*

*Corresponding author for this work

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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.
Original languageEnglish
Pages (from-to)354–367
Number of pages14
JournalApplicable Analysis
Volume97
Issue number3
DOIs
Publication statusPublished - 17-Feb-2018
Externally publishedYes

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