Decay estimates of solutions to the bipolar non-isentropic compressible Euler–Maxwell system

Abstract

We consider the global existence and large time behavior of solutions near a constant equilibrium state to the bipolar non-isentropic compressible Euler–Maxwell system in , where the background magnetic field could be non-zero. The global existence is established under the assumption that the H3 norm of the initial data is small, but its higher order derivatives could be large. Combining the negative Sobolev (or Besov) estimates with the interpolation estimates, we prove the optimal time decay rates of the solution and its higher order spatial derivatives. In this sense, our results improve the similar ones in Wang et al (2012 SIAM J. Math. Anal. 44 3429–57).