Global existence and blow-up for a weakly dissipative $\mu$DP equation

Abstract

In this paper, we study a weakly dissipative variant of the periodic Degasperis-Procesi equation. We show the local well-posedness of the associated Cauchy problem in $H^s(\S )$, $s>3/2$, and discuss the precise blow-up scenario for $s=3$. We also present explicit examples for globally existing solutions and blow-up.

11 pages

References in corpus (6)

• The hydrodynamical relevance of the Camassa-Holm and Degasperis-Procesi equations
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Cited by in corpus (1)

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