Analytic regularity of global solutions for the b-equation

TL;DR

This paper proves that for the b-equation, global solutions originating from analytic initial data remain analytic over time, regardless of the parameter choice, highlighting the regularity properties of these solutions.

Contribution

It establishes the analyticity of global solutions for the b-equation with initial data in Gevrey class, independent of the parameter value.

Findings

Global solutions are analytic in time and space for analytic initial data.

Analytic regularity holds for all real parameter choices in the b-equation.

The result applies to initial data in the Gevrey class, ensuring smoothness over time.

Abstract

In this paper, we delve into the $b$-family of equations and explore regularity properties of its global solutions. Our findings reveal that, irrespective of the real choice of the constitutive parameter, when the initial datum is confined to an analytic Gevrey function the resulting global solution is analytic in both temporal and spatial variables.