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

The entropy principle shows that, for self-gravitating perfect fluid, the Einstein field equations can be derived from extrema of total entropy, and thermodynamical stability criterion are equivalent to dynamical criterion. In this paper, we recast charged fluid in Einstein-Maxwell theory, further give star with barotropic condition. order obtain criterion, first get general formula second vari...