Long term regularity of the one-fluid Euler–Maxwell system in 3D with vorticity

Abstract

A basic model for describing plasma dynamics is given by the “one-fluid” Euler–Maxwell system, in which a compressible electron fluid interacts with its own self-consistent electromagnetic field. In this paper we prove long-term regularity of solutions of this system in 3 spatial dimensions, in the case of small initial data with nontrivial vorticity.Our main conclusion is that the time of existence of solutions depends only on the size of the vorticity of the initial data, as long as the initial data is sufficiently close to a constant stationary solution.