The conditions for the nonlinear stability of plane and helical MHD flows
type: Item
instance of: scholarly article
title: The conditions for the nonlinear stability of plane and helical MHD flows
zbMATH Open document ID: 0895.76034
DOI: 10.1016/0021-8928(95)00049-U
author: J. Ning
published in: Journal of Applied Mathematics and Mechanics
publication date: 1997-11-04T00:00:00Z
review text: The stability of steady MHD flows of ideal incompressible fluid with uniform density is investigated. The authors consider only the flows which are invariant under translational, axial, rotational or helical symmetry. The sufficient conditions for nonlinear stability of such flows with respect to perturbations possessing the corresponding symmetry are obtained. These conditions are proved by constructing functionals with an absolute minima on particular steady solutions. Each of these functionals is a sum of kinetic energy, the integral of an arbitrary function of a Lagrangian coordinate, and an integral which is specific for the flows under consideration. By using the Lagrangian coordinate fields, one obtains a family of new stability definitions. According to these definitions, deviations of perturbed flows from unperturbed ones are measured by the integrals of the squared velocity and Lagrangian coordinate perturbations. The obtained stability conditions are extended to new types of flows.
Mathematics Subject Classification ID: 76E25
Mathematics Subject Classification ID: 76W05
Mathematics Subject Classification ID: 76E30
zbMATH DE Number: 1077503
zbMATH Keywords: sufficient conditions for stability
zbMATH Keywords: symmetry
zbMATH Keywords: functionals
zbMATH Keywords: Lagrangian coordinate fields
reviewed by: Vyacheslav S. Titov
MaRDI profile type: Publication
cites work: Q5557046
cites work: Q5516802
cites work: Q3758450
cites work: Nonlinear stability of fluid and plasma equilibria
cites work: Variational principle for three-dimensional steady-state flows of an ideal fluid
full work available at URL: 0021-8928(95)00049-u
OpenAlex ID: W1994476972
description: scientific article; zbMATH DE number 1077503