The compressible Euler-Maxwell two-fluid system arises in the modeling of magnetized plasmas. We first design crucial energy functionals to capture its dissipative structure, which is relatively weaker in comparison with the one-fluid case in the whole space R3, due to the nonlinear coupling and cancelation between electrons and ions. Furthermore, with the aid of Lp(Rn)-Lq(Rn)-Lr(Rn) time-decay estimates, we obtain the L1(R3)-L2(R3) decay rate with the critical regularity (sc = 3) for the global-in-time existence of smooth solutions, which solves the decay problem left open in [Y. J. Peng, Global existence and long-time behavior of smooth solutions of two-fluid Euler-Maxwell equations, Ann. IHP Anal. Non Linéaire 29 (2012) 737-759].
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