Local existence for the non-resistive MHD equations in Besov spaces

Chemin, Jean-Yves, McCormick, David S, Robinson, James C and Rodrigo, Jose L (2016) Local existence for the non-resistive MHD equations in Besov spaces. Advances in Mathematics, 286. pp. 1-31. ISSN 0001-8708

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Abstract

In 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.

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 11:46
Last Modified: 06 Mar 2017 12:44
URI: http://sro.sussex.ac.uk/id/eprint/59612

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