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Converge rates towards stationary solutions for the outflow problem of planar magnetohydrodynamics on a half line

Part of: Partial differential equations Magnetohydrodynamics and electrohydrodynamics Functional-differential and differential-difference equations

Published online by Cambridge University Press:  17 January 2019

Haiyan Yin
Haiyan Yin*
Affiliation:
School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, P.R. China ([email protected])
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Abstract

In this paper, convergence rates of solutions towards stationary solutions for the outflow problem of planar magnetohydrodynamics (MHD) are investigated. Inspired by the relationship between MHD and Navier-Stokes, we prove that the global solutions of the planar MHD converge to the corresponding stationary solutions of Navier-Stokes equations. We obtain the corresponding convergence rates based on the weighted energy method when the initial perturbation belongs to some weighted Sobolev space.

Keywords

magnetohydrodynamicsstationary solutionsoutflow problemconvergence ratesweighted energy method

MSC classification

Primary: 35B40: Asymptotic behavior of solutions
Secondary: 34K21: Stationary solutions 76W05: Magnetohydrodynamics and electrohydrodynamics
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 149 , Issue 5 , October 2019 , pp. 1291 - 1322
Copyright
Copyright © Royal Society of Edinburgh 2019 

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