The Cauchy Problem on the Compressible Two-fluids Euler-Maxwell Equations

In this paper, we are concerned with the Cauchy problem on the compressible isentropic two-fluids Euler-Maxwell equations in three dimensions. The global existence of solutions near constant steady states with the vanishing electromagnetic field is established, and also the time-decay rates of perturbed solutions in L space for 2 ≤ q ≤ ∞ are obtained. The proof for existence is due to the classical energy method, and the investigation of the large-time behavior is based on the linearized analysis of the one-fluid Euler-Maxwell equations and the damped Euler equations. As a byproduct of our approach, some timedecay rates obtained in [18] for the nonlinear damped Euler system are improved.