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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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Abstract: This 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.
Publication Date: Feb-2017
Electronic Publication Date: 1-Sep-2016
Citation: Fefferman, 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/s00205-016-1042-7
DOI: doi:10.1007/s00205-016-1042-7
ISSN: 0003-9527
EISSN: 1432-0673
Pages: 677 - 691
Type of Material: Journal Article
Journal/Proceeding Title: ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
Version: Final published version. This is an open access article.



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