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

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posted on 2023-06-09, 00:15 authored by Jean-Yves Chemin, David S McCormick, James C Robinson, Jose L Rodrigo
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.

History

Publication status

  • Published

File Version

  • Accepted version

Journal

Advances in Mathematics

ISSN

0001-8708

Publisher

Elsevier

Volume

286

Page range

1-31

Department 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

2017-01-12

First Open Access (FOA) Date

2017-01-12

First Compliant Deposit (FCD) Date

2017-01-12

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