The optimal time‐decay estimate of solutions to two‐fluid Euler‐Maxwell equations in the critical Besov space

We obtain the optimal time‐decay rate of classical solutions to two‐fluid Euler‐Maxwell equations inR N ( N = 2 , 3 ) , which is a remaining question in the framework of critical Besov space (see [1]). The system is of regularity‐loss , so it is difficult to get decay rates in the solution space. In this paper, the new estimate of L p ‐ L q ‐ L r type and something like “square formula of Duhamel principle” are mainly used. It is shown that in the critical Besov space, the solution decays to constant equilibrium at the rate( 1 + t ) − N 2 ( 1 p − 1 2 )with 1 ≤ p < 6 / 5 if N = 3 and p = 1 if N = 2 .