Asymptotical behavior of bipolar non-isentropic compressible Navier-Stokes-Poisson system

Abstract

The bipolar non-isentropic compressible Navier-Stokes-Poisson (BNSP) system is investigated in R3 in the present paper, and the optimal L 2 time decay rate for the global classical solution is established. It is shown that the total densities, total momenta and total temperatures of two carriers converge to the equilibrium states at the rate $${\left( {1 + t} \right)^{ - \frac{3}{4} + \varepsilon }}$$ in L 2-norm for any small and fix e > 0. But, both the difference of densities and the difference of temperatures of two carriers decay at the optimal rate $${\left( {1 + t} \right)^{ - \frac{3}{4}}}$$ , and the difference of momenta decays at the optimal rate $${\left( {1 + t} \right)^{ - \frac{1}{4}}}$$ . This phenomenon on the charge transport shows the essential difference between the non-isentropic unipolar NSP and the bipolar NSP system.