Communications in Mathematical Sciences

Volume 18 (2020)

Number 2

Regularity results for the Navier–Stokes–Maxwell system

Pages: 339 – 358

DOI: https://dx.doi.org/10.4310/CMS.2020.v18.n2.a3

Authors

Zhihong Wen (Department of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, Jiangsu, China)

Zhuan Ye (Department of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, Jiangsu, China)

Abstract

In this paper, we study the Cauchy problem of the incompressible Navier–Stokes–Maxwell system with Ohm’s law in two and three space-dimensions. On the one hand, we establish an improved regularity criterion based on the velocity for the three-dimensional Navier–Stokes–Maxwell system. On the other hand, we establish the global regularity result for the Navier–Stokes–Maxwell system with the dissipation strength at the logarithmically supercritical level both in two and three space-dimensions.

Keywords

Navier–Stokes–Maxwell system, regularity criterion, global regularity

2010 Mathematics Subject Classification

35B45, 35B65, 35Q35, 76W05

Received 5 December 2018

Accepted 4 October 2019

Published 20 June 2022