The Library
Local existence for the non-resistive MHD equations in nearly optimal Sobolev spaces
Tools
Fefferman, Charles L., McCormick, David S., Robinson, James C. and Rodrigo, Jose L. (2017) Local existence for the non-resistive MHD equations in nearly optimal Sobolev spaces. Archive for Rational Mechanics and Analysis, 223 (2). pp. 677-691. doi:10.1007/s00205-016-1042-7 ISSN 0003-9527.
PDF
WRAP_art%3A10.1007%2Fs00205-016-1042-7.pdf - Published Version - Requires a PDF viewer. Available under License Creative Commons Attribution 4.0. Download (776Kb) |
|
PDF
MHDssmo-revised.pdf - Accepted Version Embargoed item. Restricted access to Repository staff only - Requires a PDF viewer. Download (279Kb) |
Official URL: http://dx.doi.org/10.1007/s00205-016-1042-7
Abstract
This paper establishes the local-in-time existence and uniqueness of solutions to the viscous, non-resistive magnetohydrodynamics (MHD) equations in RdRd , where d = 2, 3, with initial data B0∈Hs(Rd)B0∈Hs(Rd) and u0∈Hs−1+ϵ(Rd)u0∈Hs−1+ϵ(Rd) for s>d/2s>d/2 and any 0<ϵ<10<ϵ<1 . The proof relies on maximal regularity estimates for the Stokes equation. The obstruction to taking ϵ=0ϵ=0 is explained by the failure of solutions of the heat equation with initial data u0∈Hs−1u0∈Hs−1 to satisfy u∈L1(0,T;Hs+1)u∈L1(0,T;Hs+1) ; we provide an explicit example of this phenomenon.
Item Type: | Journal Article | ||||||||
---|---|---|---|---|---|---|---|---|---|
Subjects: | Q Science > QC Physics | ||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
Library of Congress Subject Headings (LCSH): | Magnetohydrodynamics, Equations -- Numerical solutions | ||||||||
Journal or Publication Title: | Archive for Rational Mechanics and Analysis | ||||||||
Publisher: | Springer | ||||||||
ISSN: | 0003-9527 | ||||||||
Official Date: | February 2017 | ||||||||
Dates: |
|
||||||||
Volume: | 223 | ||||||||
Number: | 2 | ||||||||
Page Range: | pp. 677-691 | ||||||||
DOI: | 10.1007/s00205-016-1042-7 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Open Access (Creative Commons) | ||||||||
Date of first compliant deposit: | 17 August 2016 | ||||||||
Date of first compliant Open Access: | 1 November 2016 | ||||||||
Funder: | Leverhulme Trust (LT), National Science Foundation (U.S.) (NSF), European Research Council (ERC) | ||||||||
Grant number: | Grant RPG-2015-69 (LT), Grant DMS-09-01040 (NSF), Grant 616797 (ERC) |
Request changes or add full text files to a record
Repository staff actions (login required)
View Item |
Downloads
Downloads per month over past year