Hölder Continuity for the Fokas–Olver–Rosenau–Qiao Equation

Abstract

It has been shown that the Cauchy problem for the Fokas–Olver–Rosenau–Qiao equation is well-posed for initial data \(u_0\in H^s\), \(s>5/2\), with its data-to-solution map \(u_0\mapsto u\) being continuous but not uniformly continuous. This work further investigates the continuity properties of the solution map and shows that it is Holder continuous in the \(H^r\) topology when \(0\le r<s\). The Holder exponent is given explicitly and depends on both \(s\) and \(r\).