Stability of solitary waves and weak rotation limit for the Ostrovsky equation
type: Item
instance of: scholarly article
title: Stability of solitary waves and weak rotation limit for the Ostrovsky equation
zbMATH Open document ID: 1064.35148
author: Yue Liu
author: V. V. Varlamov
published in: Journal of Differential Equations
publication date: 2004-08-20T00:00:00Z
review text: This paper is concerned with the Ostrovsky equation, which can be written in the form \((u_t - \beta u_{xxx} + (u^2)_x)_x = \gamma u\) for some constants \(\beta, \gamma \in \mathbb R\) with \(\gamma >0\). This equation describes the propagation of long internal surface waves in shallow water in the presence of a rotation. The authors consider a model where dispersion is considered but dissipation is neglected. They classify the existence and nonexistence of the dispersion parameter and prove that the set of solitary waves is stable with respect to perturbation in the case of positive dispersion. They also investigate the issue of passing to the limit as the rotation parameter tends to zero for solutions of the Cauchy problem on a bounded time interval.
reviewed by: Min Ho Lee
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 37K45
Mathematics Subject Classification ID: 35K35
Mathematics Subject Classification ID: 35Q51
Mathematics Subject Classification ID: 76B55
zbMATH DE Number: 2093542
zbMATH Keywords: long internal waves
zbMATH Keywords: dispersion
zbMATH Keywords: rotation
zbMATH Keywords: Cauchy problem
MaRDI profile type: Publication
full work available at URL: j.jde.2004.03.026
OpenAlex ID: W2031401634
cites work: Q3995225
cites work: On the Surface Waves in a Shallow Channel with an Uneven Bottom
cites work: Solitary waves of generalized Kadomtsev-Petviashvili equations
cites work: Q4440482
cites work: Stability of Coulomb systems with magnetic fields. I: The one-electron atom
cites work: On the existence of stationary solitary waves in a rotating fluid
cites work: Approximate Analytical and Numerical Solutions of the Stationary Ostrovsky Equation
cites work: Evolution Equations for Weakly Nonlinear, Long Internal Waves in a Rotating Fluid
cites work: Solitary waves of a coupled Korteweg-de Vries system
cites work: Q5621188
cites work: Q3342896
cites work: Commutator estimates and the euler and navier-stokes equations
cites work: Stability and instability of fourth-order solitary waves
cites work: On the lowest eigenvalue of the Laplacian for the intersection of two domains
cites work: The concentration-compactness principle in the calculus of variations. The locally compact case. I
cites work: On generalized Benjamin type equations
cites work: Q5752153
cites work: Stable standing waves of nonlinear Klein-Gordon equations
cites work: Cauchy problem for the Ostrovsky equation
DOI: 10.1016/J.JDE.2004.03.026
description: scientific article; zbMATH DE number 2093542