Convergence rate estimates for the low Mach and Alfven number three-scale singular limit of compressible ideal magnetohydrodynamics

Bin Cheng; Qiangchang Ju; Steve Schochet

doi:10.1051/m2an/2020051

Convergence rate estimates for the low Mach and Alfven number three-scale singular limit of compressible ideal magnetohydrodynamics

Bin Cheng, Qiangchang Ju Steve Schochet

ESAIM: Mathematical Modelling & Numerical Analysis (ESAIM: M2AN), Vol.55, pp.S733-S759

2021

: https://doi.org/10.1051/m2an/2020051

Mathematics, Applied

Science & Technology

Mathematics

Physical Sciences

Convergence rate estimates are obtained for singular limits of the compressible ideal magnetohydrodynamics equations, in which the Mach and Alfven numbers tend to zero at different rates. The proofs use a detailed analysis of exact and approximate fast, intermediate, and slow modes together with improved estimates for the solutions and their time derivatives, and the time-integration method. When the small parameters are related by a power law the convergence rates are positive powers of the Mach number, with the power varying depending on the component and the norm. Exceptionally, the convergence rate for two components involve the ratio of the two parameters, and that rate is proven to be sharp via corrector terms. Moreover, the convergence rates for the case of a power-law relation between the small parameters tend to the two-scale convergence rate as the power tends to one. These results demonstrate that the issue of convergence rates for three-scale singular limits, which was not addressed in the authors' previous paper, is much more complicated than for the classical two-scale singular limits.

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https://doi.org/10.1051/m2an/2020051

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: Convergence rate estimates for the low Mach and Alfven number three-scale singular limit of compressible ideal magnetohydrodynamics
: Bin Cheng - University of Surrey, School of Maths and Physics
Qiangchang Ju - Institute of Applied Physics and Computational Mathematics
Steve Schochet - Tel Aviv University
: ESAIM: Mathematical Modelling & Numerical Analysis (ESAIM: M2AN), Vol.55, pp.S733-S759
: Edp Sciences S A
: 27
: 2021
: IE150886 / UK Royal Society "International Exchanges" scheme; Royal Society UK RPG-2017-098 / Leverhulme Trust EP/R029628/1 / EPSRC; UK Research & Innovation (UKRI); Engineering & Physical Sciences Research Council (EPSRC) 2519/17 / ISF-NSFC joint research program (ISF) 11571046; 11471028; 11671225 / NSFC; National Natural Science Foundation of China (NSFC) 11761141008 / ISF-NSFC joint research program (NSFC)
: 99512090102346; WOS:000622089000025
: Department of Mathematics; School of Maths and Physics
: English
: Journal article