Global well-posedness and optimal decay rates of classical solutions to the compressible Navier-Stokes-Fourier-P₁ approximation model in radiation hydrodynamics

2024/12/22 by Peng Jiang, Fucai Li, Jiang, Peng +3
Mathematics · Engineering · #Navier-Stokes equation solutions #Advanced Mathematical Physics Problems #Computational Fluid Dynamics and Aerodynamics

paper · pdf · doi:10.48550/arxiv.2412.17017

Abstract

In this paper, the compressible Navier-Stokes-Fourier-P₁ (NSF-P₁) approximation model in radiation hydrodynamics is investigated in the whole space ℝ³. This model consists of the compressible NSF equations of fluid coupled with the transport equations of the radiation field propagation. Assuming that the initial data are a small perturbation near the equilibrium state, we establish the global well-posedness of classical solutions for this model by performing the Fourier analysis techniques and employing the delicate energy estimates in frequency spaces. Here, we develop a new method to overcome a series of difficulties arising from the linear terms n₁ in (3.2)₂ and n₀ in (3.3)₃ related to the radiation intensity. Furthermore, if the L¹-norm of the initial data is bounded, we obtain the optimal time decay rates of the classical solution at L^p-norm (2≤ p≤ ∞). To the best of our knowledge, this is the first result on the global well-posedness of the NSF-P₁ approximation model.

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