Global existence and decay rates of strong solutions to the diffusion approximation model in radiation hydrodynamics
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| Format: | Preprint |
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2024
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| _version_ | 1866909722416775168 |
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| author | Jiang, Peng Li, Fucai Ni, Jinkai |
| author_facet | Jiang, Peng Li, Fucai Ni, Jinkai |
| contents | In this paper, we study the global well-posedness and optimal time decay rates of strong solutions to the diffusion approximation model in radiation hydrodynamics in $\mathbb{R}^3$. This model consists of the full compressible Navier-Stokes equations and the radiative diffusion equation which describes the influence and interaction between thermal radiation and fluid motion. Supposing that the initial perturbation around the equilibrium is sufficiently small in $H^2$-norm, we obtain the global strong solutions by utilizing method of the frequency decomposition. Moreover, by performing Fourier analysis techniques and using the delicate energy method, we consequently derive the optimal decay rates (including highest-order derivatives) of solutions for this model. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_11117 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Global existence and decay rates of strong solutions to the diffusion approximation model in radiation hydrodynamics Jiang, Peng Li, Fucai Ni, Jinkai Analysis of PDEs 76N15, 76N10, 35B40 In this paper, we study the global well-posedness and optimal time decay rates of strong solutions to the diffusion approximation model in radiation hydrodynamics in $\mathbb{R}^3$. This model consists of the full compressible Navier-Stokes equations and the radiative diffusion equation which describes the influence and interaction between thermal radiation and fluid motion. Supposing that the initial perturbation around the equilibrium is sufficiently small in $H^2$-norm, we obtain the global strong solutions by utilizing method of the frequency decomposition. Moreover, by performing Fourier analysis techniques and using the delicate energy method, we consequently derive the optimal decay rates (including highest-order derivatives) of solutions for this model. |
| title | Global existence and decay rates of strong solutions to the diffusion approximation model in radiation hydrodynamics |
| topic | Analysis of PDEs 76N15, 76N10, 35B40 |
| url | https://arxiv.org/abs/2412.11117 |