Strong diffusive limit of the Boltzmann equation with Maxwell boundary condition
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arXiv
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| Format: | Preprint |
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2018
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| _version_ | 1866911337791094784 |
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| author | Guo, Yan Jung, Junhwa Zhou, Fujun |
| author_facet | Guo, Yan Jung, Junhwa Zhou, Fujun |
| contents | While weak diffusive limit from the Boltzmann equation to the incompressible Navier-Stokes-Fourier system was established for the Maxwell boundary condition within renormalized solutions framework [Saint.Raymond2009][Jiang-Masmoudi2017], the corresponding strong diffusive limit has remained outstanding except when the accommodation coefficient $α\sim \varepsilon^{1/2}$ [Jiang-Masmoudi2017]. We establish global in time strong diffusive limit for all accommodation coefficients $α\in [0, 1]$ within strong solutions framework. The main novelties of our proof include: (1) a $\varepsilon$-stretching method for reduction to a single-bounce $L^\infty$ estimate; (2) a dissipation estimate for a carefully constructed rotating Maxwellian in the near-specular regime $α\ll \varepsilon$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1809_06763 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Strong diffusive limit of the Boltzmann equation with Maxwell boundary condition Guo, Yan Jung, Junhwa Zhou, Fujun Analysis of PDEs 35Q20, 35Q83 While weak diffusive limit from the Boltzmann equation to the incompressible Navier-Stokes-Fourier system was established for the Maxwell boundary condition within renormalized solutions framework [Saint.Raymond2009][Jiang-Masmoudi2017], the corresponding strong diffusive limit has remained outstanding except when the accommodation coefficient $α\sim \varepsilon^{1/2}$ [Jiang-Masmoudi2017]. We establish global in time strong diffusive limit for all accommodation coefficients $α\in [0, 1]$ within strong solutions framework. The main novelties of our proof include: (1) a $\varepsilon$-stretching method for reduction to a single-bounce $L^\infty$ estimate; (2) a dissipation estimate for a carefully constructed rotating Maxwellian in the near-specular regime $α\ll \varepsilon$. |
| title | Strong diffusive limit of the Boltzmann equation with Maxwell boundary condition |
| topic | Analysis of PDEs 35Q20, 35Q83 |
| url | https://arxiv.org/abs/1809.06763 |