Well-posedness of the two-phase flow problem in incompressible MHD

Changyan Li; Hui Li

doi:10.3934/dcds.2021090

Article Contents

2021, Volume 41, Issue 12: 5609-5632. Doi: 10.3934/dcds.2021090 open access

This issue Previous Article Classification of transitive group actions Next Article Period tripling and quintupling renormalizations below $ C^2 $ space

Well-posedness of the two-phase flow problem in incompressible MHD

Changyan Li^1, and
Hui Li^2, ,

1.
School of Mathematical Sciences, Peking University, Beijing 100871, China
2.
Department of Mathematics, Zhejiang University, Hangzhou 310027, China

^* Corresponding author: Hui Li
^* Corresponding author: Hui Li

Received: September 2020

Revised: April 2021

Early access: June 2021

Published: December 2021

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Abstract

In this paper, we study the two phase flow problem in the ideal incompressible magnetohydrodynamics. We propose a Syrovatskij type stability condition, and prove the local well-posedness of the two phase flow problem with initial data satisfies such condition. This result shows that the magnetic field has a stabilizing effect on Kelvin-Helmholtz instability even the fluids on each side of the free interface have different densities.

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Mathematics Subject Classification: Primary: 35Q35; Secondary: 76W05.

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