Special macroscopic modes and hypocoercivity
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arXiv
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| Hauptverfasser: | , , , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866929415223508992 |
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| author | Carrapatoso, Kleber Dolbeault, Jean Hérau, Frédéric Mischler, Stéphane Mouhot, Clément Schmeiser, Christian |
| author_facet | Carrapatoso, Kleber Dolbeault, Jean Hérau, Frédéric Mischler, Stéphane Mouhot, Clément Schmeiser, Christian |
| contents | We study linear inhomogeneous kinetic equations with an external confining potential and a collision operator admitting several local conservation laws (local density, momentum and energy). We classify all special macroscopic modes (stationary solutions and time-periodic solutions). We also prove the convergence of all solutions of the evolution equation to such non-trivial modes, with a quantitative exponential rate. This is the first hypocoercivity result with multiple special macroscopic modes with constructive estimates depending on the geometry of the potential. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2105_04855 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Special macroscopic modes and hypocoercivity Carrapatoso, Kleber Dolbeault, Jean Hérau, Frédéric Mischler, Stéphane Mouhot, Clément Schmeiser, Christian Analysis of PDEs Mathematical Physics 82C40, 76P05, 35Q83, 82C70 We study linear inhomogeneous kinetic equations with an external confining potential and a collision operator admitting several local conservation laws (local density, momentum and energy). We classify all special macroscopic modes (stationary solutions and time-periodic solutions). We also prove the convergence of all solutions of the evolution equation to such non-trivial modes, with a quantitative exponential rate. This is the first hypocoercivity result with multiple special macroscopic modes with constructive estimates depending on the geometry of the potential. |
| title | Special macroscopic modes and hypocoercivity |
| topic | Analysis of PDEs Mathematical Physics 82C40, 76P05, 35Q83, 82C70 |
| url | https://arxiv.org/abs/2105.04855 |