Large-time behaviour of solutions to the magneto-hydrodynamics equations
type: Item
instance of: scholarly article
title: Large-time behaviour of solutions to the magneto-hydrodynamics equations
zbMATH Open document ID: 0846.35018
DOI: 10.1007/BF01446316
author: Tomas P. Schonbek
author: Endre Süli
author: Maria E. Schonbek
published in: Mathematische Annalen
publication date: 1996-07-09T00:00:00Z
full work available at URL: https://eudml.org/doc/165426
review text: We establish lower and upper bounds for the rate of decay of the total energy and of the magnetic energy of solutions to the magnetohydrodynamics equations on \(\mathbb{R}^n\), \(2\leq n\leq 4\). It is shown that weak solutions subject to large initial data outside a class of functions with total radially equidistributed energy decay algebraically (rather than exponentially). It is also proved that initial data with radially equidistributed energy gives rise to weak solutions which decay exponentially (rather than algebraically).
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 76W05
Mathematics Subject Classification ID: 35Q35
zbMATH DE Number: 892571
zbMATH Keywords: decay of the total energy
MaRDI profile type: Publication
cites work: Partial regularity of suitable weak solutions of the navier-stokes equations
cites work: Q5518219
cites work: On \(L^ 2\) decay of weak solutions of the Navier-Stokes equations in \(\mathbb R^ n\)
cites work: Weak and classical solutions of the two-dimensional magnetohydrodynamic equations
cites work: On energy inequality, smoothness and large time behavior in L 2 for weak solutions of the Navier-Stokes equations in exterior domains
cites work: Magnetostatic equilibria and analogous Euler flows of arbitrarily complex topology. Part 1. Fundamentals
cites work: Decay of solution to parabolic conservation laws
cites work: \(L^ 2\) decay for weak solutions of the Navier-Stokes equations
cites work: Large time behaviour of solutions to the navier-stokes equations
cites work: Lower Bounds of Rates of Decay for Solutions to the Navier-Stokes Equations
cites work: Some mathematical questions related to the mhd equations
cites work: Q3766216
cites work: Infinite-dimensional dynamical systems in mechanics and physics
cites work: Decay Results for Weak Solutions of the Navier-Stokes Equations on Rn
cites work: Sharp Rate of Decay of Solutions to 2-Dimensional Navier-Stokes Equations
OpenAlex ID: W2009787879
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description: scientific article; zbMATH DE number 892571