Diffusive Limit of the Vlasov-Poisson-Boltzmann System without Angular Cutoff
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911876953145344 |
|---|---|
| author | Xu, Yuan Zhou, Fujun Li, Yongsheng |
| author_facet | Xu, Yuan Zhou, Fujun Li, Yongsheng |
| contents | Diffusive limit of the Vlasov-Poisson-Boltzmann system without angular cutoff in the framework of perturbation around global Maxwellian still remains open. By employing the weighted energy method with a newly introduced weight function $w_l(α,β)$ and some novel treatments, we solve this problem for the full range of non-cutoff potentials $γ>-3$ and $0<s<1$. Uniform estimate with respect to the Knudsen number $\varepsilon \in (0,1]$ is established globally in time, which eventually leads to the global existence of solutions to the Vlasov-Poisson-Boltzmann system without angular cutoff for the full range of non-cutoff potentials and hydrodynamic limit to the two-fluid incompressible Navier-Stokes-Fourier-Poisson system with Ohm's law. As a byproduct, this approach also extends the global existence results of previous studies on the Vlasov-Poisson-Boltzmann system without angular cutoff to the full range of non-cutoff potentials $γ>-3$ and $0<s<1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_16588 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Diffusive Limit of the Vlasov-Poisson-Boltzmann System without Angular Cutoff Xu, Yuan Zhou, Fujun Li, Yongsheng Analysis of PDEs 35Q20, 35Q83 Diffusive limit of the Vlasov-Poisson-Boltzmann system without angular cutoff in the framework of perturbation around global Maxwellian still remains open. By employing the weighted energy method with a newly introduced weight function $w_l(α,β)$ and some novel treatments, we solve this problem for the full range of non-cutoff potentials $γ>-3$ and $0<s<1$. Uniform estimate with respect to the Knudsen number $\varepsilon \in (0,1]$ is established globally in time, which eventually leads to the global existence of solutions to the Vlasov-Poisson-Boltzmann system without angular cutoff for the full range of non-cutoff potentials and hydrodynamic limit to the two-fluid incompressible Navier-Stokes-Fourier-Poisson system with Ohm's law. As a byproduct, this approach also extends the global existence results of previous studies on the Vlasov-Poisson-Boltzmann system without angular cutoff to the full range of non-cutoff potentials $γ>-3$ and $0<s<1$. |
| title | Diffusive Limit of the Vlasov-Poisson-Boltzmann System without Angular Cutoff |
| topic | Analysis of PDEs 35Q20, 35Q83 |
| url | https://arxiv.org/abs/2312.16588 |