Contents Online
Communications in Mathematical Sciences
Volume 14 (2016)
Number 5
Decay estimates of solutions to the compressible Navier–Stokes–Maxwell system in $\mathbb{R}^3$
Pages: 1189 – 1212
DOI: https://dx.doi.org/10.4310/CMS.2016.v14.n5.a1
Authors
Abstract
The compressible Navier–Stokes–Maxwell system with linear damping is investigated in $\mathbb{R}^3$, and the global existence and large-time behavior of solutions are established. We first construct the global unique solution under the assumptions that the $H^3$ norm of the initial data is small but that the higher-order derivatives can be arbitrarily large. Further, if the initial data belongs to $\dot{H}^{-s} (0 \leq s \lt 3/2)$ or $\dot{B}^{-s}_{2,\infty} (0 \lt s \leq 3/2)$, by a regularity interpolation trick, we obtain the various decay rates of the solution and its higher-order derivatives. As an immediate by-product, the $L^p - L^2 (1 \leq p \leq 2)$ type of the decay rates follow without requiring that the $L^p$ norm of initial data is small.
Keywords
compressible Navier–Stokes–Maxwell system, global solution, time decay rate, energy method, interpolation
2010 Mathematics Subject Classification
35B40, 35Q30, 35Q35, 35Q61, 76N10, 82D37
Published 18 May 2016