Hydrodynamic limit for the non-cutoff Boltzmann equation
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866913270776987648 |
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| author | Cao, Chuqi Carrapatoso, Kleber |
| author_facet | Cao, Chuqi Carrapatoso, Kleber |
| contents | This work deals with the non-cutoff Boltzmann equation for all type of potentials, in both the torus $\mathbf{T}^3$ and in the whole space $\mathbf{R}^3$, under the incompressible Navier-Stokes scaling. We first establish the well-posedness and decay of global mild solutions to this rescaled Boltzmann equation in a perturbative framework, that is for solutions close to the Maxwellian, obtaining in particular integrated-in-time regularization estimates. We then combine these estimates with spectral-type estimates in order to obtain the strong convergence of solutions to the non-cutoff Boltzmannn equation towards the incompressible Navier-Stokes-Fourier system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_06362 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Hydrodynamic limit for the non-cutoff Boltzmann equation Cao, Chuqi Carrapatoso, Kleber Analysis of PDEs This work deals with the non-cutoff Boltzmann equation for all type of potentials, in both the torus $\mathbf{T}^3$ and in the whole space $\mathbf{R}^3$, under the incompressible Navier-Stokes scaling. We first establish the well-posedness and decay of global mild solutions to this rescaled Boltzmann equation in a perturbative framework, that is for solutions close to the Maxwellian, obtaining in particular integrated-in-time regularization estimates. We then combine these estimates with spectral-type estimates in order to obtain the strong convergence of solutions to the non-cutoff Boltzmannn equation towards the incompressible Navier-Stokes-Fourier system. |
| title | Hydrodynamic limit for the non-cutoff Boltzmann equation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2304.06362 |