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

Abstract

Dissipative hyperbolic systems of \textit{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 $s_c=5/2$, that is, the extra higher regularity is not needed.

25 pages. arXiv admin note: text overlap with arXiv:1503.06291

References in corpus (3)

• The Boltzmann equation, Besov spaces, and optimal time decay rates in the whole space
• Global classical solutions for partially dissipative hyperbolic system of balance laws
• Decay structure for symmetric hyperbolic systems with non-symmetric relaxation and its application