Optimal decay rate of the incompressible Navier–Stokes–Maxwell system with Ohm’s law

Abstract

This work is to establish optimal time decay rate of global classical solutions to the two-fluid incompressible Navier–Stokes–Maxwell system with Ohm’s law and the incompressible Navier–Stokes–Maxwell system with Ohm’s law in R3. The results show that the optimal time decay rate for the velocity of these two systems achieves the same as that of the incompressible Navier–Stokes equation. In other words, Ohm’s law can offset the negative effects brought by the Maxwell equation on the decay rate of solutions. This is interesting compared to the compressible Navier–Stokes system, whose time decay rate decreases when it is coupled with the self-consistent Maxwell system.