Decay estimates of solutions to the compressible Euler-Maxwell system in R3

Abstract

We study the large time behavior of solutions near a constant equilibrium to the compressible Euler-Maxwell system in $\mathring{3}$. We first refine a global existence theorem by assuming that the $H^3$ norm of the initial data is small, but the higher order derivatives can be arbitrarily large. If the initial data belongs to $\Dot{H}^{-s}$ ($0\le s<3/2$) or ${\dot{B}}_{2,\infty }^{-s}$ ($0<s\le 3/2$), by a regularity interpolation trick, we obtain the various decay rates of the solution and its higher order derivatives. As an immediate byproduct, the usual $L^p$--$L^2$ $(1\le p\le 2)$ type of the decay rates follow without requiring that the $L^p$ norm of initial data is small.

22 pages, typos are fixed, Journal of Differential Equations (2015)

References in corpus (1)

• The Boltzmann equation, Besov spaces, and optimal time decay rates in the whole space

Cited by in corpus (1)

• The well-posedness of the compressible non-isentropic Euler-Maxwell system in R^3