Methods and Applications of Analysis

Volume 18 (2011)

Number 3

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

Pages: 245 – 268

DOI: https://dx.doi.org/10.4310/MAA.2011.v18.n3.a1

Authors

Shuichi Kawashima (Faculty of Mathematics, Kyushu University, Fukuoka, Japan)

Yoshihiro Ueda (Faculty of Maritime Sciences, Kobe University, Kobe, Japan)

Abstract

We study the decay property for the Euler-Maxwell system in $R³$ 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 $H^s ∩ L¹$ with enough regularity $s ≥ 6$. The proof is based on the time weighted energy method combined with the semigroup approach.

Keywords

Euler-Maxwell system, decay estimate, regularity-loss, energy method

2010 Mathematics Subject Classification

35B35, 35B40, 35L40, 82D10

Published 5 April 2012