Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6425489 | Advances in Mathematics | 2016 | 31 Pages |
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 u0âB2,1n/2â1 and B0âB2,1n/2. The a priori estimates include the term â«0tâu(s)âHn/22ds on the right-hand side, which thus requires an auxiliary bound in Hn/2â1. 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.
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Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Jean-Yves Chemin, David S. McCormick, James C. Robinson, Jose L. Rodrigo,