Analyticity of the Cauchy problem and persistence properties for a generalized Camassa-Holm equation

TL;DR

This paper proves the analyticity and persistence of solutions for a generalized Camassa-Holm equation with analytic initial data, demonstrating global-in-space analyticity and providing asymptotic profiles to confirm the results' optimality.

Contribution

It establishes the analyticity of solutions in both variables and persistence properties for the generalized Camassa-Holm equation, with explicit asymptotic profiles confirming the results' optimality.

Findings

Solutions are analytic in both variables globally in space and locally in time.

Persistence properties for strong solutions are established.

Asymptotic profiles demonstrate the optimality of the analyticity and persistence results.

Abstract

This paper is mainly concerned with the Cauchy problem for a generalized Camassa-Holm equation with analytic initial data. The analyticity of its solutions is proved in both variables, globally in space and locally in time. Then, we present a persistence property for strong solutions to the system. Finally, explicit asymptotic profiles illustrate the optimality of these results.