L3,∞-solutions to the MHD equations

Alex Mahalov; B. Nicolaenko; T. Shilkin

doi:10.1007/s10958-007-0175-5

L_3,∞-solutions to the MHD equations

Alex Mahalov, B. Nicolaenko, T. Shilkin

Research output: Contribution to journal › Article › peer-review

23 Scopus citations

Abstract

We prove that weak solutions to the MHD system are smooth provided that they belong to the so-called "critical" Ladyzhenskaya-Prodi-Serrin class L_3,∞. Besides the independent interest, this result disproves the hypothesis on existence of collapsing self-similar solutions to the MHD equations for which the generating profile belongs to the space L ₃. Thus, we extend the results which were known before for the Navier-Stokes system to the case of the MHD equations. Bibliography: 14 titles.

Original language	English (US)
Pages (from-to)	2911-2923
Number of pages	13
Journal	Journal of Mathematical Sciences
Volume	143
Issue number	2
DOIs	https://doi.org/10.1007/s10958-007-0175-5
State	Published - May 2007

ASJC Scopus subject areas

Statistics and Probability
General Mathematics
Applied Mathematics

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abstract = "We prove that weak solutions to the MHD system are smooth provided that they belong to the so-called {"}critical{"} Ladyzhenskaya-Prodi-Serrin class L3,∞. Besides the independent interest, this result disproves the hypothesis on existence of collapsing self-similar solutions to the MHD equations for which the generating profile belongs to the space L 3. Thus, we extend the results which were known before for the Navier-Stokes system to the case of the MHD equations. Bibliography: 14 titles.",

author = "Alex Mahalov and B. Nicolaenko and T. Shilkin",

note = "Funding Information: This research was supported by CRDF RU-M1-2596-ST-04. The third autor was also supported by the RFBR (project 05-01-00941) and by the Russian Science Support Foundation.",

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AU - Mahalov, Alex

AU - Nicolaenko, B.

AU - Shilkin, T.

N1 - Funding Information: This research was supported by CRDF RU-M1-2596-ST-04. The third autor was also supported by the RFBR (project 05-01-00941) and by the Russian Science Support Foundation.

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N2 - We prove that weak solutions to the MHD system are smooth provided that they belong to the so-called "critical" Ladyzhenskaya-Prodi-Serrin class L3,∞. Besides the independent interest, this result disproves the hypothesis on existence of collapsing self-similar solutions to the MHD equations for which the generating profile belongs to the space L 3. Thus, we extend the results which were known before for the Navier-Stokes system to the case of the MHD equations. Bibliography: 14 titles.

AB - We prove that weak solutions to the MHD system are smooth provided that they belong to the so-called "critical" Ladyzhenskaya-Prodi-Serrin class L3,∞. Besides the independent interest, this result disproves the hypothesis on existence of collapsing self-similar solutions to the MHD equations for which the generating profile belongs to the space L 3. Thus, we extend the results which were known before for the Navier-Stokes system to the case of the MHD equations. Bibliography: 14 titles.

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L_3,∞-solutions to the MHD equations

Abstract

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