Abstract: We consider an interface with surface tension that separates a perfectly conducting inviscid fluid from a vacuum. The fluid flow is governed by the equations of ideal compressible magnetohydrodynamics (MHD), while the electric and magnetic fields in vacuum satisfy the Maxwell equations. With boundary conditions on the interface this forms a nonlinear hyperbolic problem with a characteristic free boundary. For the corresponding linearized problem we derive an energy a priori estimate in a conormal Sobolev space without assuming any stability conditions on the unperturbed flow. This verifies the stabilizing effect of surface tension because, as was shown in [11], a sufficiently large vacuum electric field can make the linearized problem ill-posed for the case of zero surface tension. The main ingredients in proving the energy estimate are a suitable secondary symmetrization of the Maxwell equations in vacuum and making full use of the boundary regularity enhanced from the surface tension.

Cite: Trakhinin Y.
Stabilizing effect of surface tension for the linearized MHD–Maxwell free interface problem
Journal of Differential Equations. 2025. V.427. P.143-162. DOI: 10.1016/j.jde.2025.01.086 WOS Scopus OpenAlex

Dates:

Submitted:	Sep 23, 2024
Accepted:	Jan 26, 2025
Published online:	Jan 31, 2025
Published print:	May 15, 2025

Identifiers:

Web of science:	WOS:001421167600001
Scopus:	2-s2.0-85216478915
OpenAlex:	W4407023540

Citing: Пока нет цитирований

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