On the Radius of Analyticity for a Korteweg-de Vries-Kawahara Equation with a Weakly Damping Term

TL;DR

This paper investigates the analyticity radius of solutions to a Korteweg-de Vries-Kawahara equation with damping, establishing local and global well-posedness and showing the analyticity radius remains uniformly positive over time.

Contribution

It introduces new estimates in analytic Bourgain spaces and proves the uniform lower bound of the analyticity radius for solutions over time.

Findings

Local well-posedness in Gevrey spaces

Global extension with positive analyticity radius

Use of approximate conservation law for bounds

Abstract

We consider the Cauchy problem for an equation of Korteweg-de Vries-Kawahara type with initial data in the analytic Gevrey spaces. By using linear, bilinear and trilinear estimates in analytic Bourgain spaces, we establish the local well-posedness for this problem. By using an approximate conservation law, we extend this to a global result in such a way that the radius of analyticity of solutions is uniformly bounded below by a fixed positive number for all time.