Long‐time behavior of solution for the compressible Navier‐Stokes‐Maxwell equations in

Abstract

In this paper, we are concerned with optimal decay rates for higher‐order spatial derivatives of classical solution to the compressible Navier‐Stokes‐Maxwell equations in three‐dimensional whole space. If the initial perturbation is small in H3∩L1‐norm, we apply the Fourier splitting method to establish optimal decay rates for the second‐order spatial derivatives of a solution. As a by‐product, the rate of classical solution converging to the constant equilibrium state in L∞‐norm is false(1+tfalse)−32.

Local well‐posedness of the isentropic Navier‐Stokes‐Maxwell system with vacuum

“…Fan et al considered the vanishing limits of dielectric constant or the Mach number . Chen et al and Mi and Gao established the long‐time asymptotic behavior of the smooth solutions.…”