CoupledParabolicElliptic.pdf (345.75 kB)
Existence and uniqueness for a coupled parabolic-elliptic model with applications to magnetic relaxation
journal contribution
posted on 2023-06-09, 00:16 authored by David S McCormick, James C Robinson, Jose L RodrigoWe prove existence, uniqueness and regularity of weak solutions of a coupled parabolic-elliptic model in 2D, and existence of weak solutions in 3D; we consider the standard equations of magnetohydrodynamics with the advective terms removed from the velocity equation. Despite the apparent simplicity of the model, the proof in 2D requires results that are at the limit of what is available, including elliptic regularity in $L^{1}$ and a strengthened form of the Ladyzhenskaya inequality () which we derive using the theory of interpolation. The model potentially has applications to the method of magnetic relaxation introduced by Moffatt (J. Fluid. Mech. 159, 359–378, 1985) to construct stationary Euler flows with non-trivial topology.
History
Publication status
- Published
File Version
- Accepted version
Journal
Archive for Rational Mechanics and AnalysisISSN
0003-9527Publisher
Springer VerlagExternal DOI
Issue
2Volume
214Page range
503-523Department 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
Categories
No categories selectedKeywords
Licence
Exports
RefWorks
BibTeX
Ref. manager
Endnote
DataCite
NLM
DC