Nonuniform dependence of the R‐b‐family system in Besov spaces

Abstract

AbstractIn this paper, we consider a generalized rotation b‐family system (R‐b‐family system) which models the evolution of equatorial water waves. Based on local well‐posedness results and lifespan estimates, we establish sharpness of continuity on the data‐to‐solution map by showing that it is not uniformly continuous from to . The proof of nonuniform dependence is based upon approximate solutions and Littlewood‐Paley decomposition theory.