Blow-up criteria for a two-component nonlinear dispersive wave system


Novruzov E., Bayrak V.

JOURNAL OF FUNCTIONAL ANALYSIS, vol.282, no.12, 2022 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 282 Issue: 12
  • Publication Date: 2022
  • Doi Number: 10.1016/j.jfa.2022.109454
  • Title of Journal : JOURNAL OF FUNCTIONAL ANALYSIS
  • Keywords: Nonlinear dispersive wave equation, Rod equation, Blow-up, Shallow water, SHALLOW-WATER EQUATION, GLOBAL WEAK SOLUTIONS, WELL-POSEDNESS, BREAKING WAVES, EXISTENCE, PERMANENT

Abstract

We investigate the blow-up phenomena for the two-component generalizations of nonlinear dispersive wave equation on the real line that includes the two-component Camassa-Holm system as well as the system for the hyperelasticrod wave equation as special cases. We establish a blowup criterion for system of coupled equations under certain natural initial profiles. The obtained criterion involves only the properties of the data u0 in a neighbourhood of a single point and consequently, it is local-in-space with respect to first component of the system under consideration. (C)2022 Elsevier Inc. All rights reserved.