The two-fluid incompressible Navier–Stokes–Maxwell system: Green’s function and optimal decay rate

Abstract

In this paper, we consider the two-fluid incompressible Navier–Stokes–Maxwell system in three dimensional space. The analysis shows that the effect of the Lorentz force induced by the electromagnetic field leads to some different structures of the spectrum. Moreover, the detailed analysis of the Green’s function to the linearized system is made with applications to derive the optimal time decay rate of the solution converging to the steady state.