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

Abstract

Dissipative hyperbolic systems of 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 decayregularity for dissipative systems. As an application, it is shown that the optimal decay rate of L 1 (R 3 )-L 2 (R 3 ) is available for Euler-Maxwell equations with the critical regularity s c = 5/2, that is, the extra higher regularity is not needed.