Communications in Mathematical Sciences

Volume 16 (2018)

Number 2

Global classical solutions to the two-fluid incompressible Navier–Stokes–Maxwell system with Ohm’s law

Pages: 561 – 578

DOI: https://dx.doi.org/10.4310/CMS.2018.v16.n2.a12

Authors

Ning Jiang (School of Mathematics and Statistics, Wuhan University, Wuhan, China)

Yi-Long Luo (School of Mathematics and Statistics, Wuhan University, Wuhan, China)

Abstract

We study the global in time classical solutions to the two-fluid incompressible Navier–Stokes–Maxwell system with (solenoidal) Ohm’s law with small initial data. This system is a coupling of the incompressible Navier–Stokes equations with the Maxwell equations through the Lorenz force and Ohm’s law for the current. In this proof, we employ the decay properties of both the electric field $E$ and the wave equation with linear damping of the divergence free magnetic field $B$.

Keywords

Navier–Stokes–Maxwell system, Ohm’s law, global classical solution

2010 Mathematics Subject Classification

35A01, 35A09, 35B45, 35Q35, 35Q61, 76D05, 76K05

Full Text (PDF format)

This work was supported by the grants from the National Natural Science Foundation of China under contract No. 11471181 and No. 11731008.

Received 21 September 2017

Accepted 14 January 2018

Published 14 May 2018