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

Dissipative hyperbolic systems of $\mathit{\text{regularity-loss}}$ have been recently received increasing attention. Usually, extra higher regularity is assumed to obtain the optimal decay estimates, in comparison with that for 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 $L^1({\mathbb{R}}^3)$-$L^2({\mathbb{R}}^3)$ is available for Euler-Maxwell equations with the critical regularity $s_c=5\mathrm{/}2$, that is, the extra higher regularity is not needed.