BesovMHDPaper - After referee report.pdf (362.12 kB)
Local existence for the non-resistive MHD equations in Besov spaces
journal contribution
posted on 2023-06-09, 00:15 authored by Jean-Yves Chemin, David S McCormick, James C Robinson, Jose L RodrigoIn this paper we prove the existence of solutions to the viscous, non-resistive magnetohydrodynamics (MHD) equations on the whole of Rn, n = 2, 3, for divergence-free initial data in certain Besov spaces, namely u0 ? Bn/2-1 2,1 and B0 ? Bn/2 2,1. The a priori estimates include the term t 0 u(s) 2 Hn/2 ds on the right-hand side, which thus requires an auxiliary bound in Hn/2-1. In 2D, this is simply achieved using the standard energy inequality; but in 3D an auxiliary estimate in H1/2 is required, which we prove using the splitting method of Calderón (1990) [2]. By contrast, our proof that such solutions are unique only applies to the 3D case.
History
Publication status
- Published
File Version
- Accepted version
Journal
Advances in MathematicsISSN
0001-8708Publisher
ElsevierExternal DOI
Volume
286Page range
1-31Department affiliated with
- Mathematics Publications
Research groups affiliated with
- Numerical Analysis and Scientific Computing Research Group Publications
Full text available
- Yes
Peer reviewed?
- Yes
Legacy Posted Date
2017-01-12First Open Access (FOA) Date
2017-01-12First Compliant Deposit (FCD) Date
2017-01-12Usage metrics
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