Global well-posedness and optimal decay rates of classical solutions to the compressible Navier-Stokes-Fourier-P$_1$ approximation model in radiation hydrodynamics
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| Format: | Preprint |
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2024
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| author | Jiang, Peng Li, Fucai Ni, Jinkai |
| author_facet | Jiang, Peng Li, Fucai Ni, Jinkai |
| contents | In this paper, the compressible Navier-Stokes-Fourier-$P_1$ (NSF-$P_1$) approximation model in radiation hydrodynamics is investigated in the whole space $\mathbb{R}^3$. 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 $n_1$ in (3.2)$_2$ and $n_0$ in (3.3)$_3$ related to the radiation intensity. Furthermore, if the $L^1$-norm of the initial data is bounded, we obtain the optimal time decay rates of the classical solution at $L^p$-norm $(2\leq p\leq \infty)$. To the best of our knowledge, this is the first result on the global well-posedness of the NSF-$P_1$ approximation model. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_17017 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Global well-posedness and optimal decay rates of classical solutions to the compressible Navier-Stokes-Fourier-P$_1$ approximation model in radiation hydrodynamics Jiang, Peng Li, Fucai Ni, Jinkai Analysis of PDEs 76N15, 76N10, 35B40 In this paper, the compressible Navier-Stokes-Fourier-$P_1$ (NSF-$P_1$) approximation model in radiation hydrodynamics is investigated in the whole space $\mathbb{R}^3$. 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 $n_1$ in (3.2)$_2$ and $n_0$ in (3.3)$_3$ related to the radiation intensity. Furthermore, if the $L^1$-norm of the initial data is bounded, we obtain the optimal time decay rates of the classical solution at $L^p$-norm $(2\leq p\leq \infty)$. To the best of our knowledge, this is the first result on the global well-posedness of the NSF-$P_1$ approximation model. |
| title | Global well-posedness and optimal decay rates of classical solutions to the compressible Navier-Stokes-Fourier-P$_1$ approximation model in radiation hydrodynamics |
| topic | Analysis of PDEs 76N15, 76N10, 35B40 |
| url | https://arxiv.org/abs/2412.17017 |