Global analytic solutions of a pseudospherical Novikov equation

Abstract

In this paper we consider a Novikov equation, recently shown to describe pseudospherical surfaces, to extend some recent results of regularity of its solutions. By making use of the global well-posedness in Sobolev spaces, for analytic initial data in Gevrey spaces we prove some new estimates for the solution in order to use the Kato–Masuda Theorem and obtain a lower bound for the radius of spatial analyticity. After that, we use embeddings between spaces to then conclude that the unique solution is, in fact, globally analytic in both variables. Finally, the global analyticity of the solution is used to prove that it endows the strip $(0,\infty )\times R$ with a global analytic metric associated to pseudospherical surfaces obtained in Sales Filho and Freire (2022).