On the wellposedness of the Navier-Stokes-Maxwell system

2012/07/26 by Pierre Germain, Germain, Pierre, Slim Ibrahim +3
Mathematics · #35Q30 #35Q61 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35Q30 #msc:35Q61

paper · pdf · doi:10.48550/arxiv.1207.6187

16 pages

arxiv created 2012/07/26 · arxiv updated 2012/07/27

Abstract

We study the local and global wellposedness of a full system of Magneto-Hydro-Dynamic equations. The system is a coupling of the forced (Lorentz force) incompressible Navier-Stokes equations with the Maxwell equations through Ohm's law for the current. We show the local existence of mild solutions for arbitrarily large data in a space similar to the scale invariant spaces classically used for Navier-Stokes. These solutions are global if the initial data are small enough.

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