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

Abstract

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 the time-decay rates of perturbed solutions in $L^q$ space for $2\leq q\leq \infty$ are obtained. The proof for existence is due to the classical energy method, and the investigation of large-time behavior is based on linearized analysis of one-fluid Euler–Maxwell equations and damped Euler equations. As a byproduct of our approach, some time-decay rates obtained by Sideris, Thomases, and Wang [Comm. Partial Differential Equations, 28 (2003), pp. 795–816] for the nonlinear damped Euler system are improved.