Nonlinear Stability of MHD Contact Discontinuities with Surface Tension

Yuri Trakhinin, Tao Wang

Результат исследования: Научные публикации в периодических изданияхстатьярецензирование

Аннотация

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.

Язык оригиналаанглийский
Страницы (с-по)1091-1149
Число страниц59
ЖурналArchive for Rational Mechanics and Analysis
Том243
Номер выпуска2
DOI
СостояниеОпубликовано - февр. 2022

Предметные области OECD FOS+WOS

  • 1.01 МАТЕМАТИКА
  • 2.03 МЕХАНИКА И МАШИНОСТРОЕНИЕ

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