Well-posedness of the Navier-Stokes-Maxwell equations

作者：Germain Pierre^*; Ibrahim Slim; Masmoudi Nader

来源：Proceedings of the Royal Society of Edinburgh: Section A Mathematics , 2014, 144(1): 71-86.

DOI：10.1017/S0308210512001242

We study the local and global well-posedness of a full system of magnetohydrodynamic equations. The system is a coupling of the incompressible Navier-Stokes equations with the Maxwell equations through the Lorentz force and 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. Our results not only simplify and unify the proofs for the space dimensions 2 and 3, but also refine those in [8]. The main simplification comes from an a priori L-t(2) (L-x(infinity)) estimate for solutions of the forced Navier-Stokes equations.

• 出版日期2014-2