Attracting curves on families of stationary solutions in two-dimensional Navier-Stokes and reduced magnetohydrodynamics

Derks, Gianne and Ratiu, Tudor (1998) Attracting curves on families of stationary solutions in two-dimensional Navier-Stokes and reduced magnetohydrodynamics Proceedings of the Royal Society of London A, 454. pp. 1407-1444.

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Abstract

Families of stable stationary solutions of the two-dimensional incompressible homogeneous Euler and ideal reduced magnetohydrodynamic equations are shown to be attracting for the corresponding viscous perturbations of these systems, i.e. for the Navier-Stokes and the reduced viscous MHD equations with magnetic diffusion. Each solution curve of the dissipative system starting in a cone around the family of stationary solutions of the unperturbed conservative system defines a shadowing curve which attracts the dissipative solution in an exponential manner. As a consequence, the specific exponential decay rates are also determined. The techniques to analyse these two equations can be applied to other dissipative perturbations of Hamiltonian systems. The method in its general setting is also presented.

Item Type:	Article
Divisions :	Faculty of Engineering and Physical Sciences > Mathematics
Authors :	Name Email ORCID Derks, Gianne g.derks@surrey.ac.uk Ratiu, Tudor
Date :	8 May 1998
Uncontrolled Keywords :	Navier-Stokes, magnetohydrodynamics, attractors, stability, Euler's equations, shadowing
Additional Information :	Published in Proceedings of the Royal Society of London A, 454, 1407-1444. © 1998 The Royal Society.
Depositing User :	Mr Adam Field
Date Deposited :	27 May 2010 14:40
Last Modified :	16 Jan 2019 16:21
URI:	http://epubs.surrey.ac.uk/id/eprint/1364

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