𝐿_{𝑝}-estimates of the solution of a linear problem arising in magnetohydrodynamics

Solonnikov, V.

doi:10.1090/S1061-0022-2011-01191-4

$L_p$-estimates of the solution of a linear problem arising in magnetohydrodynamics
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by V. Solonnikov
Translated by: the author

St. Petersburg Math. J. 23 (2012), 161-177

DOI: https://doi.org/10.1090/S1061-0022-2011-01191-4

Published electronically: November 10, 2011

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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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