Nonlinear stability of rotating patterns
type: Item
instance of: scholarly article
title: Nonlinear stability of rotating patterns
zbMATH Open document ID: 1173.35018
author: Wolf-Jürgen Beyn
author: Jens Lorenz
published in: Dynamics of Partial Differential Equations
publication date: 2009-03-04T00:00:00Z
review text: The author consider \(2D\) localized rotating patterns which solve a coupled system of parabolic PDEs on the spatial domain \(\mathbb R^2\). They suggest the conditions that provide the nonlinear stability of solutions with asymptotic phase with respect to the norm in the Sobolev space \(H^2\). The stability result is obtained by a combination of energy and resolvent estimates, after the dynamics is decomposed into an evolution within a three-dimensional group orbit and a transversal evolution towards the group orbit. An application of the obtained stability result to the quintic-cubic Ginzburg-Landau equation is also discussed. In addition the relevant numerical computations are presented.
reviewed by: Michael I. Gil'
Mathematics Subject Classification ID: 35B35
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 35K60
Mathematics Subject Classification ID: 58J70
zbMATH DE Number: 5523329
zbMATH Keywords: parabolic equations
zbMATH Keywords: rotating patterns
zbMATH Keywords: nonlinear stability
zbMATH Keywords: asymptotic stability
zbMATH Keywords: Ginzburg-Landau equation
zbMATH Keywords: decomposition of dynamics
zbMATH Keywords: energy and resolvent estimates
zbMATH Keywords: quintic-cubic Ginzburg-Landau equation
MaRDI profile type: Publication
full work available at URL: dpde.2008.v5.n4.a4
OpenAlex ID: W2029367552
DOI: 10.4310/DPDE.2008.V5.N4.A4
description: scientific article; zbMATH DE number 5523329