Global existence and blow-up for a weakly dissipative μμDP equation

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 Hs(S)Hs(S), s>3/2s>3/2, and discuss the precise blow-up scenario for s=3s=3. We also present explicit examples for globally existing solutions and blow-up.