Blow-up phenomena and local well-posedness for a generalized Camassa-Holm equation

Abstract

In this paper we mainly study the Cauchy problem for a generalized Camassa-Holm equation. First, by using the Littlewood-Paley decomposition and transport equations theory, we establish the local well-posedness for the Cauchy problem of the equation in Besov spaces. Then we give a simply blow-up criterion for the Cauchy problem of the equation. we present a blow-up result and the exact blow-up rate of strong solutions to the equation by making use of the conservation law and the obtained blow-up criterion.Finally, we verify that the system possesses peakon solutions.

References in corpus (5)

• An integrable shallow water equation with peaked solitons
• The hydrodynamical relevance of the Camassa-Holm and Degasperis-Procesi equations
• Multi-peakon solutions of the Degasperis-Procesi equation
• On asymptotically equivalent shallow water wave equations
• Local well-posedness and blow-up criteria for a two-component Novikov system in the critical Besov space