On the localization of the magnetic and the velocity fields in the equations of magnetohydrodynamics

Details On the localization of the magnetic and the velocity fields in the equations of magnetohydrodynamics On the localization of the magnetic and the velocity fields in the equations of magnetohydrodynamics

2006-04-13

arxiv.org/abs/math/0604310v1

Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 2007, 137 (2006) 475--495

Mathematics

Analysis of PDEs

Proceedings of the Royal Society of Edinburgh. Section A. Mathematics (to appear) (0000) --xx--

Scientific paper

We study the behavior at infinity, with respect to the space variable, of solutions to the magnetohydrodynamics equations in ${\bf R}^d$. We prove that if the initial magnetic field decays sufficiently fast, then the plasma flow behaves as a solution of the free nonstationnary Navier--Stokes equations when $|x|\to +\infty$, and that the magnetic field will govern the decay of the plasma, if it is poorly localized at the beginning of the evolution. Our main tools are boundedness criteria for convolution operators in weighted spaces.

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