Decay property of regularity-loss type for the Euler-Maxwell system

Abstract

Abstract. We study the decay property for the Euler-Maxwell system in R 3 and observe that it is of the regularity-loss type. We show that the solution decays at the rate t −3/4 as t → ∞, provided that the initial data are in H s ∩ L 1 with enough regularity s ≥ 6. The proof is based on the time weighted energy method combined with the semigroup approach.

Uniform global existence and convergence of Euler-Maxwell systems with small parameters

“…Another important problem concerns the global existence of smooth solutions when the parameters are fixed and the initial data are in a small neighborhood of the constant equilibrium state (1, 0, 0, B e ), which is a particular solution of system (2), where B e ∈ R 3 is any given constant. In [32] (see also [12,41,33]), the authors established a global existence result near such a constant equilibrium. This result did not take into account the dependence with respect to the parameters τ and γ.…”

“…* We use the fact h (n) ≥κ > 0 to obtain (40). * We use the first compatibility equation in (2) to obtain (41). * We use inequality (4) to obtain (42).…”

Global Existence and Asymptotic Behavior of Solutions for Compressible Two-Fluid Euler–Maxwell Equation

“…Two hierarchies of models of the ionospheric plasma for twofluid Euler-Maxwell equations were presented in [9]. e Fourier transform method was considered by Duan [2,10] and Kawashima and Ueda [11]. Jerome [12] adapted the classical semigroup-resolvent approach of Kato [13] to the Cauchy problem in R 3 and established a local smooth solution.…”