Existence and uniqueness for a coupled parabolic-elliptic model with applications to magnetic relaxation

McCormick, David S, Robinson, James C and Rodrigo, Jose L (2015) Existence and uniqueness for a coupled parabolic-elliptic model with applications to magnetic relaxation. Archive for Rational Mechanics and Analysis, 214 (2). pp. 503-523. ISSN 0003-9527

[img] PDF - Accepted Version
Download (354kB)

Abstract

We 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.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Research Centres and Groups: Numerical Analysis and Scientific Computing Research Group
Subjects: Q Science > QA Mathematics > QA0299 Analysis. Including analytical methods connected with physical problems
Depositing User: David McCormick
Date Deposited: 12 Jan 2017 11:39
Last Modified: 07 Mar 2017 20:29
URI: http://sro.sussex.ac.uk/id/eprint/59611

View download statistics for this item

📧 Request an update