Local well-posedness for the periodic Boltzmann equation with constant collision kernel
| Autor: | Başakoğlu, Engin, Tzvetkov, Nikolay, Sun, Chenmin, Wang, Yuzhao |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We study the Boltzmann equation with the constant collision kernel in the case of spatially periodic domain $\mathbb{T}^d$, $d\geq 2$. Using the existing techniques from nonlinear dispersive PDEs, we prove the local well-posedness result in $L^{2,r}_vH^s_x$ for $s>\frac{d}{2}-\frac{1}{4}$ and $r>\frac{d}{2}$. To reach the result, the main tool we establish is the $L^4$ Strichartz estimate for solutions to the corresponding linear equation. |
| Databáze: | arXiv |
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