Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Well-posedness of the linearized plasma-vacuum interface problem in ideal incompressible MHD


Authors: Alessandro Morando, Yuri Trakhinin and Paola Trebeschi
Journal: Quart. Appl. Math. 72 (2014), 549-587
MSC (2000): Primary 76W05; Secondary 35Q35, 35L50, 76E17, 76E25, 35R35, 76B03
DOI: https://doi.org/10.1090/S0033-569X-2014-01346-7
Published electronically: April 22, 2014
MathSciNet review: 3237563
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Abstract: We study the free boundary problem for the plasma-vacuum interface in ideal incompressible magnetohydrodynamics (MHD). In the vacuum region the magnetic field is described by the div-curl system of pre-Maxwell dynamics, while at the interface the total pressure is continuous and the magnetic field is tangent to the boundary. Under a suitable stability condition satisfied at each point of the plasma-vacuum interface, we prove the well-posedness of the linearized problem in Sobolev spaces.


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Additional Information

Alessandro Morando
Affiliation: Dipartimento di Matematica, Facoltà di Ingegneria, Università di Brescia, Via Valotti, 9, 25133 Brescia, Italy
Email: alessandro.morando@unibs.it

Yuri Trakhinin
Affiliation: Sobolev Institute of Mathematics, Koptyug av. 4, 630090 Novosibirsk, Russia
Email: trakhin@math.nsc.ru

Paola Trebeschi
Affiliation: Dipartimento di Matematica, Facoltà di Ingegneria, Università di Brescia, Via Valotti, 9, 25133 Brescia, Italy
Email: paola.trebeschi@unibs.it

DOI: https://doi.org/10.1090/S0033-569X-2014-01346-7
Received by editor(s): July 6, 2012
Received by editor(s) in revised form: August 30, 2012
Published electronically: April 22, 2014
Additional Notes: Part of this work was done during the fellowship of Y.T. at the Landau Network–Centro Volta–Cariplo Foundation spent at the Department of Mathematics of the University of Brescia in Italy. Y.T. would like to warmly thank the Department of Mathematics of the University of Brescia for its kind hospitality during the visiting period. Research of Y.T. was also partially supported under RFBR (Russian Foundation for Basic Research) grant number 10-01-00320-a
Article copyright: © Copyright 2014 Brown University

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