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) [11] to Besov spaces and is consistent with the present work (J. Math. Fluid Mech., 2020) [17] on Novikov equation up to some coefficients when dropping the extra term (∂ x u) 3 in FORQ.