Anomalous smoothing effect on the incompressible Navier-Stokes-Fourier limit from Boltzmann with periodic velocity
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866916256132628480 |
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| author | Gu, Zhongyang Hu, Xin Yoneda, Tsuyoshi |
| author_facet | Gu, Zhongyang Hu, Xin Yoneda, Tsuyoshi |
| contents | Adding some nontrivial terms composed from a microstructure, we prove the existence of a global-in-time weak solution, whose enstrophy is bounded for all the time, to an incompressible 3D Navier-Stokes-Fourier system for arbitrary initial data. It cannot be expected to directly derive the energy inequality for this new system of equations. The main idea is to employ the hydrodynamic limit from the Boltzmann equation with periodic velocity and a specially designed collision operator. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2308_00363 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Anomalous smoothing effect on the incompressible Navier-Stokes-Fourier limit from Boltzmann with periodic velocity Gu, Zhongyang Hu, Xin Yoneda, Tsuyoshi Analysis of PDEs 35Q20, 76P05, 35Q30, 76D05 Adding some nontrivial terms composed from a microstructure, we prove the existence of a global-in-time weak solution, whose enstrophy is bounded for all the time, to an incompressible 3D Navier-Stokes-Fourier system for arbitrary initial data. It cannot be expected to directly derive the energy inequality for this new system of equations. The main idea is to employ the hydrodynamic limit from the Boltzmann equation with periodic velocity and a specially designed collision operator. |
| title | Anomalous smoothing effect on the incompressible Navier-Stokes-Fourier limit from Boltzmann with periodic velocity |
| topic | Analysis of PDEs 35Q20, 76P05, 35Q30, 76D05 |
| url | https://arxiv.org/abs/2308.00363 |