$l^{2}$-decoupling and the unconditional uniqueness for the Boltzmann equation
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866915972838850560 |
|---|---|
| author | Chen, Xuwen Shen, Shunlin Zhang, Zhifei |
| author_facet | Chen, Xuwen Shen, Shunlin Zhang, Zhifei |
| contents | We broaden the application of the $l^{2}$-decoupling theorem to the Boltzmann equation. We prove Strichartz estimates for the linear problem in the $\mathbb{T}^d$ setting. We establish space-time bilinear estimates, and hence the unconditional uniqueness of solutions to the $\mathbb{R}^d$ and $\mathbb{T}^d$ Boltzmann equation for the Maxwellian particle and soft potential with an angular cutoff, adopting a unified hierarchy scheme originally developed for the nonlinear Schrödinger equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_14697 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $l^{2}$-decoupling and the unconditional uniqueness for the Boltzmann equation Chen, Xuwen Shen, Shunlin Zhang, Zhifei Analysis of PDEs We broaden the application of the $l^{2}$-decoupling theorem to the Boltzmann equation. We prove Strichartz estimates for the linear problem in the $\mathbb{T}^d$ setting. We establish space-time bilinear estimates, and hence the unconditional uniqueness of solutions to the $\mathbb{R}^d$ and $\mathbb{T}^d$ Boltzmann equation for the Maxwellian particle and soft potential with an angular cutoff, adopting a unified hierarchy scheme originally developed for the nonlinear Schrödinger equation. |
| title | $l^{2}$-decoupling and the unconditional uniqueness for the Boltzmann equation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2501.14697 |