Compressible non-isentropic bipolar navier–stokes–poisson system in ℝ3

The compressible non-isentropic bipolar Navier–Stokes–Poisson (BNSP) system is investigated in ℝ3 in the present paper, and the optimal time decay rates of global strong solution are shown. For initial data being a perturbation of equilibrium state in for l ≤ 4 and s ∈ (0, 1], it is shown that the density and temperature for each charged particle (like electron or ion) decay at the same optimal rate (1 + t)−¾, but the momentum for each particle decays at the optimal rate which is slower than the rate for the compressible Navier–Stokes (NS) equations [19] for same initial data. However, the total momentum tends to the constant state at the rate (1 + t)−¾ as well, due to the interplay interaction of charge particles which counteracts the influence of electric field.