Decay rate of strong solutions to compressible Navier-Stokes-Poisson equations with external force
Texas State University, Department of Mathematics
In this article, we consider the three dimensional compressible Navier-Stokes-Poisson equations with the effect of external potential force. First, the stationary solution is established by solving a nonlinear elliptic system. Next, we show global well-posedness of the strong solutions for the initial value problem to the three dimensional compressible Navier-Stokes-Poisson equations when the initial data are close to the stationary solution in H2(ℝ3)-norm of initial perturbation is finite, we prove the optimal Lp(ℝ3) (2 ≤ p ≤ 6) decay rates for such strong solution and L2(ℝ3) decay rate of its first-order spatial derivatives via a low frequency and high frequency decomposition.
Navier-Stokes-Poisson equation, Stationary solution, Strong solution, Energy estimate, Optimal decay rate
Li, Y., & Zhang, N. (2019). Decay rate of strong solutions to compressible Navier-Stokes-Poisson equations with external force. <i>Electronic Journal of Differential Equations, 2019</i>(61), pp. 1-18.