Well-posedness and global existence for a generalized Degasperis–Procesi equation

Abstract

We first establish the local existence and uniqueness of strong solutions for the Cauchy problem of a generalized Degasperis–Procesi equation in nonhomogeneous Besov spaces by using the Littlewood–Paley theory. Then, we prove the solution depends continuously on the initial data. Finally, we derive a blow-up criterion and present a global existence result for the equation.