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

TL;DR

This paper demonstrates that the solution map for the Fokas-Olver-Rosenau-Qiao equation is not uniformly continuous in Besov spaces, extending prior results from Sobolev spaces and relating to Novikov equation behavior.

Contribution

It extends the non-uniform continuity results of the FORQ equation from Sobolev to Besov spaces, clarifying the equation's well-posedness properties.

Findings

Solution map not uniformly continuous in Besov spaces

Extension of previous Sobolev space results

Relation to Novikov equation behavior

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 $(\partial_xu)^3$ in FORQ.