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$ L_p$-estimates of the solution of a linear problem arising in magnetohydrodynamics


Author: V. Solonnikov
Translated by: the author
Original publication: Algebra i Analiz, tom 23 (2011), nomer 1.
Journal: St. Petersburg Math. J. 23 (2012), 161-177
MSC (2010): Primary 35Q35
DOI: https://doi.org/10.1090/S1061-0022-2011-01191-4
Published electronically: November 10, 2011
MathSciNet review: 2760153
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Abstract | References | Similar Articles | Additional Information

Abstract: Coercive estimates in anisotropic Sobolev spaces $ W_p^{2,1}(Q_T)$ are established for solutions of a linearized problem of magnetohydrodynamics for the magnetic field. The result can help analyze nonlinear problems of magnetohydrodymanics, in particular, free boundary problems.


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Additional Information

V. Solonnikov
Affiliation: St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, Petersburg 191023, Russia
Email: solonnik@pdmi.ras.ru

DOI: https://doi.org/10.1090/S1061-0022-2011-01191-4
Keywords: Coercive estimates, magnetohydrodynamics
Received by editor(s): October 19, 2010
Published electronically: November 10, 2011
Dedicated: Dedicated to the memory of M. Sh. Birman
Article copyright: © Copyright 2011 American Mathematical Society