Abstract: We study the local well-posedness for an interface with surface tension that separates a perfectly conducting inviscid fluid from a vacuum. The fluid flow is governed by the equations of three-dimensional ideal compressible magnetohydrodynamics (MHD), while the vacuum magnetic and electric fields are supposed to satisfy the pre-Maxwell equations. The fluid and vacuum magnetic fields are tangential to the interface. This renders a nonlinear hyperbolic-elliptic coupled problem with a characteristic free boundary. We introduce some suitable regularization to establish the solvability and tame estimates for the linearized problem. Combining the linear well-posedness result with a modified Nash--Moser iteration scheme, we prove the local existence and uniqueness of solutions of the nonlinear problem. The non-collinearity condition required by Secchi and Trakhinin [Nonlinearity, 27 (2014), pp. 105--169] for the case of zero surface tension becomes unnecessary in our result, which verifies the stabilizing effect of surface tension on the evolution of moving vacuum interfaces in ideal compressible MHD.

Cite: Trakhinin Y. , Wang T.
Well-Posedness for Moving Interfaces with Surface Tension in Ideal Compressible MHD
SIAM Journal on Mathematical Analysis. 2022. V.54. N6. P.5888-5921. DOI: 10.1137/22m1488429 WOS Scopus РИНЦ OpenAlex

Dates:

Submitted:	Apr 4, 2022
Accepted:	Aug 5, 2022
Published print:	Nov 9, 2022
Published online:	Nov 9, 2022

Identifiers:

Web of science:	WOS:000963562000004
Scopus:	2-s2.0-85144611308
Elibrary:	59348342
OpenAlex:	W4308653790

Citing:

DB	Citing
Scopus	6
Web of science	6
OpenAlex	8

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