Pointwise Estimates Of Green Function For Non-isentropic Navier-Stokes-Poisson Equations In Three-dimensional

In this paper we derive pointwise estimates for the Green's function of the Navier-Stokes-Poisson equations for the compressible fluid.We decompose the Green's func-tion into low and high frequency waves in the Fourier space.Use the pointwise estimates we find that the large time behavior of the G(x,t)is dominated by the low frequency waves while the short time behavior oflow frequency waves consist of entropy and acoustic waves.Inside the cone C = {(x,the G(x,t)is dominated by the high frequen-cy waves.Furthermore,we find that the t):|x|<ct +(?)},G(x,t)is dominated by entropy waves t-3/2 B3/2(x,t)while outside the cone it consists of both entropy and acoustic waves:t-3/2 BN(x,t)for arbitrarily large N and t-3/2(1 + t)-1/2 BN(|x|-ct,t).This led to G(x,t)decays more slowly on the wavefront than elsewhere.As the Bessel potential of this equation of this paper is non-singular,the wave speed(?)is faster than the wave of previous Navier-Stokes equation.