The frequency-localization technique and minimal decay-regularity for Euler–Maxwell equations

Dissipative hyperbolic systems of regularity-loss   have been recently received increasing attention. Extra higher regularity is usually assumed to obtain the optimal decay estimates, in comparison with the global-in-time existence of solutions. In this paper, we develop a new frequency-localization time-decay property, which enables us to overcome the technical difficulty and improve the minimal decay-regularity for dissipative systems. As an application, it is shown that the optimal decay rate of L1(R3)L1(R3)–L2(R3)L2(R3) is available for Euler–Maxwell equations with the critical regularity sc=5/2sc=5/2, that is, the extra higher regularity is not necessary.