Local existence for the non-resistive MHD equations in nearly optimal Sobolev spaces

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. ISSN 0003-9527

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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 Rd , where d = 2, 3, with initial data B0 ∈ Hs(Rd ) and u0 ∈ Hs−1+ε(Rd ) for s > d/2 and any 0 <ε< 1. The proof relies on maximal regularity estimates for the Stokes equation. The obstruction to taking ε = 0 is explained by the failure of solutions of the heat equation with initial data u0 ∈ Hs−1 to satisfy u ∈ L1(0, T ; Hs+1); we provide an explicit example of this phenomenon.

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 12:12
Last Modified: 11 Sep 2017 15:00
URI: http://sro.sussex.ac.uk/id/eprint/66123

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Project NameSussex Project NumberFunderFunder Ref
Novel discretisations of higher-order nonlinear PDEG1603LEVERHULME TRUSTRPG-2015-069