The global well-posedness and Newtonian limit for the relativistic Boltzmann equation in a periodic box
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866909089235206144 |
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| author | Cao, Chuqi Ouyang, Jing Wang, Yong Xiao, Changguo |
| author_facet | Cao, Chuqi Ouyang, Jing Wang, Yong Xiao, Changguo |
| contents | In this paper, we study the Newtonian limit for relativistic Boltzmann equation in a periodic box $\mathbb{T}^3$. We first establish the global-in-time mild solutions of relativistic Boltzmann equation with uniform-in-$\mathfrak{c}$ estimates and time decay rate. Then we rigorously justify the global-in-time Newtonian limits from the relativistic Boltzmann solutions to the solution of Newtonian Boltzmann equation in $L^1_pL^{\infty}_x$. Moreover, if the initial data of Newtonian Boltzmann equation belong to $W^{1,\infty}(\mathbb{T}^3\times\mathbb{R}^3)$, based on a decomposition and $L^2-L^\infty$ argument, the global-in-time Newtonian limit is proved in $L^{\infty}_{x,p}$. The convergence rates of Newtonian limit are obtained both in $L^1_pL^{\infty}_x$ and $L^{\infty}_{x,p}$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_17634 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The global well-posedness and Newtonian limit for the relativistic Boltzmann equation in a periodic box Cao, Chuqi Ouyang, Jing Wang, Yong Xiao, Changguo Analysis of PDEs In this paper, we study the Newtonian limit for relativistic Boltzmann equation in a periodic box $\mathbb{T}^3$. We first establish the global-in-time mild solutions of relativistic Boltzmann equation with uniform-in-$\mathfrak{c}$ estimates and time decay rate. Then we rigorously justify the global-in-time Newtonian limits from the relativistic Boltzmann solutions to the solution of Newtonian Boltzmann equation in $L^1_pL^{\infty}_x$. Moreover, if the initial data of Newtonian Boltzmann equation belong to $W^{1,\infty}(\mathbb{T}^3\times\mathbb{R}^3)$, based on a decomposition and $L^2-L^\infty$ argument, the global-in-time Newtonian limit is proved in $L^{\infty}_{x,p}$. The convergence rates of Newtonian limit are obtained both in $L^1_pL^{\infty}_x$ and $L^{\infty}_{x,p}$. |
| title | The global well-posedness and Newtonian limit for the relativistic Boltzmann equation in a periodic box |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2401.17634 |