Regularity for the Boltzmann equation conditional to pressure and moment bounds
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916791192649728 |
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| author | Fernández-Real, Xavier Ros-Oton, Xavier Weidner, Marvin |
| author_facet | Fernández-Real, Xavier Ros-Oton, Xavier Weidner, Marvin |
| contents | We prove that solutions to the Boltzmann equation without cut-off satisfying pointwise bounds on some observables (mass, pressure, and suitable moments) enjoy a uniform bound in $L^\infty$ in the case of hard potentials. As a consequence, we derive $C^{\infty}$ estimates and decay estimates for all derivatives, conditional to these macroscopic bounds. Our $L^\infty$ estimates are uniform in the limit $s \nearrow 1$ and hence we recover the same results also for the Landau equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_03067 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Regularity for the Boltzmann equation conditional to pressure and moment bounds Fernández-Real, Xavier Ros-Oton, Xavier Weidner, Marvin Analysis of PDEs 35Q82, 76P05, 35Q20, 35R09 We prove that solutions to the Boltzmann equation without cut-off satisfying pointwise bounds on some observables (mass, pressure, and suitable moments) enjoy a uniform bound in $L^\infty$ in the case of hard potentials. As a consequence, we derive $C^{\infty}$ estimates and decay estimates for all derivatives, conditional to these macroscopic bounds. Our $L^\infty$ estimates are uniform in the limit $s \nearrow 1$ and hence we recover the same results also for the Landau equation. |
| title | Regularity for the Boltzmann equation conditional to pressure and moment bounds |
| topic | Analysis of PDEs 35Q82, 76P05, 35Q20, 35R09 |
| url | https://arxiv.org/abs/2408.03067 |