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Zapiski Nauchnykh Seminarov POMI, 2006, Volume 336, Pages 112–132
(Mi znsl199)
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This article is cited in 27 scientific papers (total in 27 papers)
$L_{3,\infty}$-solutions to the MHD equations
A. Mahalova, B. Nicolaenko, T. N. Shilkinb a Arizona State University
b St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences
Abstract:
We prove that weak solutions to the MHD system are smooth providing they belong to the so-called “critical” Ladyzhenskaya–Prodi–Serrin class $L_{3,\infty}$. Besides the independent interest, this result controverts the hypothesis on the existence of collapsing self-similar solutions to the MHD equations for which the generating profile belongs to the space $L_3$. So, we extend the results that were known before for the Navier–Stokes system, for the case of the MHD equations.
Received: 06.03.2006
Citation:
A. Mahalov, B. Nicolaenko, T. N. Shilkin, “$L_{3,\infty}$-solutions to the MHD equations”, Boundary-value problems of mathematical physics and related problems of function theory. Part 37, Zap. Nauchn. Sem. POMI, 336, POMI, St. Petersburg, 2006, 112–132; J. Math. Sci. (N. Y.), 143:2 (2007), 2911–2923
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https://www.mathnet.ru/eng/znsl199 https://www.mathnet.ru/eng/znsl/v336/p112
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Abstract page: | 290 | Full-text PDF : | 124 | References: | 50 |
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