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On the asymptotic stability of a stratified flow of the 2D non-resistive incompressible MHD equations

  • Yi DuEmail author
  • Jing Huang
  • Hao Liu
Article
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Abstract

The exponential stability of a stratified flow of the two-dimensional incompressible MHD equations on a periodic domain \({\mathbb {T}}^2=[0,1]\times [0,1]\) is presented. The stability mechanism which makes our results possible is due to the dissipation which arose from the mixing effect from the background flow. More precisely, although the magnetic field potential is governed by a transport equation, by using the algebraic structure of the incompressible condition, it turns out that the linearized MHD equation around the given stratified flow retains a non-local damping mechanism. We established the stability by combining with the energy estimates and the decay estimates.

Keywords

Stability Non-stationary stratified flow 2D MHD equations 

Mathematics Subject Classification

35Q35 35Q60 

Notes

Acknowledgements

The authors are supported by NSFC (Grant Nos. 11471126 and 11971199).

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Mathematical SciencesJinan UniversityGuangzhouChina

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