On the Cauchy Problem for a Nonlinearly Dispersive Wave Equation

2003/01/01 by Zhaoyang Yin · 1 citation
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Cauchy problem #Damped wave #Dispersive partial differential equation #Hyperbolic partial differential equation #Initial value problem #Navier-Stokes equation solutions #Nonlinear Waves and Solitons #Wave equation #Well-posed problem #math.AP

paper · pdf · doi:10.2991/jnmp.2003.10.1.2

published as J. Nonlinear Math. Phys., volume 10, no. 1 (2003) 10-15 · arxiv version is already official

openalex publication_date 2003/01/01 · arxiv created 2003/09/10 · arxiv updated 2015/06/26 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We establish the local well-posedness for a new nonlinearly dispersive wave equation and we show that the equation has solutions that exist for indefinite times as well as solutions which blowup in finite time. Furthermore, we derive an explosion criterion for the equation and we give a sharp estimate from below for the existence time of solutions with smooth initial data.

Citations

• Well-posedness and Blow-up Solutions for an Integrable Nonlinearly Dispersive Model Wave Equation
• Wave breaking for nonlinear nonlocal shallow water equations

Cited by

• Global existence of weak solutions to the Camassa-Holm equation