Pointwise estimates of solution for the Navier–Stokes–Poisson equations in multi-dimensions

The Cauchy problem of the Navier–Stokes–Poisson equations in multi-dimensions (n⩾3) is considered. We obtain the pointwise estimates of the solution when it is a perturbation of the constant state. Then we have the optimal Lp(Rn) (p⩾1) convergence rate of the solution.