On the Cauchy problem of a weakly dissipative $\mu$HS equation

Abstract

In this paper, we study the Cauchy problem of a weakly dissipative $\mu$HS equation. We first establish the local well-posedness for the weakly dissipative $\mu$HS equation by Kato's semigroup theory. Then, we derive the precise blow-up scenario for strong solutions to the equation. Moreover, we present some blow-up results for strong solutions to the equation. Finally, we give two global existence results to the equation.

References in corpus (5)

• Variational derivation of the Camassa-Holm shallow water equation
• Stability of multipeakons
• On the blow-up structure for the generalized periodic Camassa-Holm and Degasperis-Procesi equations
• Global existence and blow-up for a weakly dissipative $\mu$DP equation
• On the wave-breaking phenomena and global existence for the generalized periodic Camassa-Holm equation