Communications in Mathematical Sciences
Volume 16 (2018)
Global classical solutions to the two-fluid incompressible Navier–Stokes–Maxwell system with Ohm’s law
Pages: 561 – 578
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 $B$.
Navier–Stokes–Maxwell system, Ohm’s law, global classical solution
2010 Mathematics Subject Classification
35A01, 35A09, 35B45, 35Q35, 35Q61, 76D05, 76K05
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