Green's Function and Pointwise Space-time Behaviors of the Three-Dimensional Relativistic Boltzmann Equation
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929339267809280 |
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| author | Li, Yanchao Zhong, Mingying |
| author_facet | Li, Yanchao Zhong, Mingying |
| contents | The pointwise space-time behavior of the Green's function of the three-dimensional relativistic Boltzmann equation is studied in this paper. It is shown that the Green's function has a decomposition of the macroscopic diffusive waves and Huygens waves with the speed $\sqrt{a^2+b^2}$ at low-frequency, the singular kinetic wave and the remainder term decaying exponentially in space and time. In addition, we establish the pointwise space-time estimate of the global solution to the nonlinear relativistic Boltzmann equation with non-smooth initial data based on the Green's function. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_06280 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Green's Function and Pointwise Space-time Behaviors of the Three-Dimensional Relativistic Boltzmann Equation Li, Yanchao Zhong, Mingying Analysis of PDEs 76P05, 82C40, 82D05 The pointwise space-time behavior of the Green's function of the three-dimensional relativistic Boltzmann equation is studied in this paper. It is shown that the Green's function has a decomposition of the macroscopic diffusive waves and Huygens waves with the speed $\sqrt{a^2+b^2}$ at low-frequency, the singular kinetic wave and the remainder term decaying exponentially in space and time. In addition, we establish the pointwise space-time estimate of the global solution to the nonlinear relativistic Boltzmann equation with non-smooth initial data based on the Green's function. |
| title | Green's Function and Pointwise Space-time Behaviors of the Three-Dimensional Relativistic Boltzmann Equation |
| topic | Analysis of PDEs 76P05, 82C40, 82D05 |
| url | https://arxiv.org/abs/2405.06280 |