Methods and Applications of Analysis
Volume 18 (2011)
Decay property of regularity-loss type for the Euler-Maxwell system
Pages: 245 – 268
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 $Hs ∩ L1$ with enough regularity $s ≥ 6$. The proof is based on the time weighted energy method combined with the semigroup approach.
Euler-Maxwell system, decay estimate, regularity-loss, energy method
2010 Mathematics Subject Classification
35B35, 35B40, 35L40, 82D10