Global existence and pointwise estimates of solution for the incompressible Navier–Stokes–Poisson–Fourier system for rough initial data in R3

In this paper, the Cauchy problem of the incompressible Navier–Stokes–Poisson–Fourier (NSPF) system in dimension three is considered. First, we construct the Green’s function of the linearized NSPF system and establish its decay in both time and space. Moreover, we prove the global existence of solutions for the NSPF system in the space L∞ ∩ L2 and obtain pointwise long-time decay estimates for the solution.