TY - JOUR

T1 - Well-Posedness for Moving Interfaces with Surface Tension in Ideal Compressible MHD

AU - Trakhinin, Yuri

AU - Wang, Tao

N1 - FUNDING INFORMATION: Ministry of Science and Higher Education of the Russian Federation : 075-15-2022-282. Hong Kong Institute for Advanced Study : 9360157. Fundamental Research Funds for the Central Universities https://doi.org/10.13039/501100012226 : 2042022kf1183. National Natural Science Foundation of China https://doi.org/10.13039/501100001809 : 11731008, 11971359.

PY - 2022/12/1

Y1 - 2022/12/1

N2 - 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.

AB - 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.

KW - ideal compressible MHD

KW - moving interface

KW - pre-Maxwell equations

KW - surface tension

KW - well-posedness

UR - https://www.scopus.com/inward/record.url?eid=2-s2.0-85144611308&partnerID=40&md5=bcee3551970a3b2a6911d4d3bf8c195c

UR - https://www.mendeley.com/catalogue/4a772532-f2e7-3833-a61d-6e8e6b632215/

U2 - 10.1137/22M1488429

DO - 10.1137/22M1488429

M3 - Article

VL - 54

SP - 5888

EP - 5921

JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

SN - 0036-1410

IS - 6

ER -