The local criteria for blowup of the Dullin-Gottwald-Holm equation and the two-component Dullin-Gottwald-Holm system

TL;DR

This paper establishes new local-in-space blow-up criteria for the Dullin-Gottwald-Holm equation and its two-component system, advancing understanding of wave breaking phenomena in these nonlinear wave models.

Contribution

It introduces a novel blow-up criterion applicable to the general case, linking local initial data conditions to wave breaking in these equations.

Findings

New blow-up criterion for $oldsymbol{ ext{Dullin-Gottwald-Holm}}$ equation

Extension of criteria to the two-component system

Conditions involving local-in-space initial data for wave breaking

Abstract

We investigate wave breaking for the Dullin-Gottwald-Holm equation and the two-component Dullin-Gottwald-Holm system. We establish a new blow-up criterion for the general case $\gamma+c_0\alpha^2 \geq 0$ involving local-in-space conditions on the initial data.