Dissipative Structure of the Regularity-Loss Type and Time Asymptotic Decay of Solutions for the Euler--Maxwell System

Abstract

We consider the large-time behavior of solutions to the initial value problem for the Euler--Maxwell system in $\mathbb{R}^3$. This system verifies the decay property of the regularity-loss type. Under smallness condition on the initial perturbation, we show that the solution to the problem exists globally in time and converges to the equilibrium state as time tends to infinity. The crucial point of the proof is to derive a priori estimates of solutions by using the energy method.