Global well posedness for a two-fluid model
Abstract
We study a two fluid system which models the motion of a charged fluid with Rayleigh friction, and in the presence of an electro-magnetic field satisfying Maxwell's equations. We study the well-posdness of the system in both space dimensions two and three. Regardless of the size of the initial data, we first prove the global well-posedness of the Cauchy problem when the space dimension is two. However, in space dimension three, we construct global weak-solutions \`a la Leray, and we prove the local well-posedness of Kato-type solutions. These solutions turn out to be global when the initial data are sufficiently small. Our results extend Giga-Yoshida (1984) ones to the space dimension two, and improve them in terms of requiring less regularity on the velocity fields.
Keywords
Cite
@article{arxiv.1411.0917,
title = {Global well posedness for a two-fluid model},
author = {Yoshikazu Giga and Slim Ibrahim and Shengyi Shen and Tsuyoshi Yoneda},
journal= {arXiv preprint arXiv:1411.0917},
year = {2017}
}