Decay estimates of solutions to the compressible Euler–Maxwell system in [formula omitted

Abstract

We study the large time behavior of solutions near a constant equilibrium to the compressible Euler–Maxwell system in R3. We first refine a global existence theorem by assuming that the H3 norm of the initial data is small, but the higher order derivatives can be arbitrarily large. If the initial data belongs to H˙−s (0≤s<3/2) or B˙2,∞−s (0<s≤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 Lp–L2(1≤p≤2) type of the decay rates follows without requiring that the Lp norm of initial data is small.