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Nonlinear Stability of the Current‐Vortex Sheet to the Incompressible MHD Equations
Author(s) -
Sun Yongzhong,
Wang Wei,
Zhang Zhifei
Publication year - 2018
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.21710
Subject(s) - magnetohydrodynamics , vortex sheet , vortex , compressibility , nonlinear system , instability , mathematics , magnetic field , stability (learning theory) , ideal (ethics) , classical mechanics , current (fluid) , mechanics , current sheet , physics , mathematical analysis , vorticity , computer science , law , quantum mechanics , machine learning , thermodynamics , political science
In this paper, we solve a long‐standing open problem: nonlinear stability of the current‐vortex sheet in the ideal incompressible magnetohydrodynamics under the Syrovatskij stability condition. This result gives the first rigorous confirmation of the stabilizing effect of the magnetic field on Kelvin‐Helmholtz instability.© 2017 Wiley Periodicals, Inc.