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Local Existence for the Non-Resistive MHD Equations in Nearly Optimal Sobolev Spaces

Author(s): Fefferman, Charles L.; McCormick, David S; Robinson, James C; Rodrigo, Jose L

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dc.contributor.authorFefferman, Charles L.-
dc.contributor.authorMcCormick, David S-
dc.contributor.authorRobinson, James C-
dc.contributor.authorRodrigo, Jose L-
dc.date.accessioned2019-12-10T17:45:30Z-
dc.date.available2019-12-10T17:45:30Z-
dc.date.issued2017-02en_US
dc.identifier.citationFefferman, Charles L, McCormick, David S, Robinson, James C, Rodrigo, Jose L. (2017). Local Existence for the Non-Resistive MHD Equations in Nearly Optimal Sobolev Spaces. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 223 (677 - 691. doi:10.1007/s00205-016-1042-7en_US
dc.identifier.issn0003-9527-
dc.identifier.urihttp://arks.princeton.edu/ark:/88435/pr18x7m-
dc.description.abstractThis paper establishes the local-in-time existence and uniqueness of solutions to the viscous, non-resistive magnetohydrodynamics (MHD) equations in R-d, where d = 2, 3, with initial data B-0 is an element of H-s(R-d) and u(0) is an element of Hs-1+epsilon(R-d) for s > d/2 and any 0 < epsilon < 1. The proof relies on maximal regularity estimates for the Stokes equation. The obstruction to taking epsilon = 0 is explained by the failure of solutions of the heat equation with initial data u(0) is an element of H(s-1)t o satisfy u is an element of L-1 (0, T; Hs+1); we provide an explicit example of this phenomenon.en_US
dc.format.extent677 - 691en_US
dc.language.isoen_USen_US
dc.relation.ispartofARCHIVE FOR RATIONAL MECHANICS AND ANALYSISen_US
dc.rightsFinal published version. This is an open access article.en_US
dc.titleLocal Existence for the Non-Resistive MHD Equations in Nearly Optimal Sobolev Spacesen_US
dc.typeJournal Articleen_US
dc.identifier.doidoi:10.1007/s00205-016-1042-7-
dc.date.eissued2016-09-01en_US
dc.identifier.eissn1432-0673-
pu.type.symplectichttp://www.symplectic.co.uk/publications/atom-terms/1.0/journal-articleen_US

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