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outflow problem

Proceedings of the Royal Society of Edinburgh Section A: Mathematics (1)

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Converge rates towards stationary solutions for the outflow problem of planar magnetohydrodynamics on a half line
Part of
Haiyan Yin
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 149 / Issue 5 / October 2019

Published online by Cambridge University Press:

17 January 2019, pp. 1291-1322

Print publication:

October 2019
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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.