Open AccessWell-posedness of the two-phase flow problem in incompressible MHD
Author(s) -
Xinxin Yan,
Hui Li
Publication year - 2021
Publication title -
discrete and continuous dynamical systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.289
H-Index - 70
eISSN - 1553-5231
pISSN - 1078-0947
DOI - 10.3934/dcds.2021090
Subject(s) - magnetohydrodynamics , compressibility , physics , flow (mathematics) , magnetic field , ideal (ethics) , instability , mechanics , phase (matter) , stability (learning theory) , incompressible flow , magnetohydrodynamic drive , mathematics , classical mechanics , mathematical analysis , computer science , quantum mechanics , philosophy , epistemology , machine learning
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.