On propagation of regularities and evolution of radius of analyticity in the solution of the fifth order KdV-BBM model

TL;DR

This paper studies a fifth order KdV-BBM water wave model, proving regularity propagation, local well-posedness in Gevrey class, and analyzing how the radius of analyticity evolves over time.

Contribution

It establishes the propagation of regularity, local well-posedness in Gevrey class, and explicit bounds on the evolution of the radius of analyticity for the model.

Findings

Regularity propagates without singularities in solutions.

Local well-posedness established in Gevrey class.

Explicit formulas for bounds on the radius of analyticity.

Abstract

We consider the initial value problem (IVP) associated to a fifth order KdV-BBM type model that describes the propagation of unidirectional water waves. We prove that the regularity in the initial data propagates in the solution, in other words no singularities can appear or disappear in the solution to this model. We also prove the local well-posedness of the IVP in the space of the analytic functions, the so called Gevrey class. Furthermore, we discuss the evolution of radius of analyticity in such class by providing explicit formulas for upper and lower bounds.