Non-uniform continuity of the Fokas-Olver-Rosenau-Qiao equation in Besov spaces

Abstract

In this paper, we prove that the solution map of Fokas_Olver_Rosenau_Qiao equation (FORQ) is not uniformly continuous on the initial data in Besov spaces. Our result extends the previous non_uniform continuity in Sobolev spaces (Nonlinear Anal., 2014) to Besov spaces and is consistent with the present work (J. Math. Fluid Mech., 2020) on Novikov equation up to some coefficients when dropping the extra term $({\partial }_{x}u{)}^3$ in FORQ.

This paper has been submitted on August 19, 2020