On the wellposedness of the Navier-Stokes-Maxwell system
Analysis of PDEs
2012-07-27 v1
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.
Keywords
Cite
@article{arxiv.1207.6187,
title = {On the wellposedness of the Navier-Stokes-Maxwell system},
author = {Pierre Germain and Slim Ibrahim and Nader Masmoudi},
journal= {arXiv preprint arXiv:1207.6187},
year = {2012}
}
Comments
16 pages