TY - JOUR

T1 - Nonlinear Stability of MHD Contact Discontinuities with Surface Tension

AU - Trakhinin, Yuri

AU - Wang, Tao

N1 - Funding Information: The research of Yuri Trakhinin was supported by the Russian Science Foundation under Grant No. 20-11-20036. The research of Tao Wang was supported by the National Natural Science Foundation of China under Grants 11971359 and 11731008. Publisher Copyright: © 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH, DE, part of Springer Nature.

PY - 2022/2

Y1 - 2022/2

N2 - We consider the motion of two inviscid, compressible, and electrically conducting fluids separated by an interface across which there is no fluid flow in the presence of surface tension. The magnetic field is supposed to be nowhere tangential to the interface. This leads to the characteristic free boundary problem for contact discontinuities with surface tension in three-dimensional ideal compressible magnetohydrodynamics (MHD). We prove the nonlinear structural stability of MHD contact discontinuities with surface tension in Sobolev spaces by a modified Nash–Moser iteration scheme. The main ingredient of our proof is deriving the resolution and tame estimate of the linearized problem in usual Sobolev spaces of sufficiently large regularity. In particular, for solving the linearized problem, we introduce a suitable regularization that preserves the transport-type structure for the linearized entropy and divergence of the magnetic field.

AB - We consider the motion of two inviscid, compressible, and electrically conducting fluids separated by an interface across which there is no fluid flow in the presence of surface tension. The magnetic field is supposed to be nowhere tangential to the interface. This leads to the characteristic free boundary problem for contact discontinuities with surface tension in three-dimensional ideal compressible magnetohydrodynamics (MHD). We prove the nonlinear structural stability of MHD contact discontinuities with surface tension in Sobolev spaces by a modified Nash–Moser iteration scheme. The main ingredient of our proof is deriving the resolution and tame estimate of the linearized problem in usual Sobolev spaces of sufficiently large regularity. In particular, for solving the linearized problem, we introduce a suitable regularization that preserves the transport-type structure for the linearized entropy and divergence of the magnetic field.

UR - http://www.scopus.com/inward/record.url?scp=85122814127&partnerID=8YFLogxK

U2 - 10.1007/s00205-021-01740-6

DO - 10.1007/s00205-021-01740-6

M3 - Article

AN - SCOPUS:85122814127

VL - 243

SP - 1091

EP - 1149

JO - Archive for Rational Mechanics and Analysis

JF - Archive for Rational Mechanics and Analysis

SN - 0003-9527

IS - 2

ER -