What question did this study set out to answer?

This research aims to analyze the Cauchy problem for the incompressible Navier–Stokes–Poisson–Fourier system in three dimensions.

May 9, 2026

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

Key Points

This research aims to analyze the Cauchy problem for the incompressible Navier–Stokes–Poisson–Fourier system in three dimensions.
Constructed the Green's function for the linearized NSPF system.
Established decay properties in both time and space.
Demonstrated global existence of solutions in L∞ ∩ L2 space.
Proved global existence of solutions under specific initial data conditions.
Obtained pointwise long-time decay estimates for the NSPF system solution.

Abstract

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.

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