The Cauchy problem for the inhomogeneous non-cutoff Kac equation in critical Besov space
| Autor: | Hao-Guang Li, Chao-Jiang Xu, Jiang Xu, Hongmei Cao |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Applied Mathematics
Weak solution 010102 general mathematics Mathematical analysis Mathematics::Analysis of PDEs Perturbation (astronomy) Geodetic datum 01 natural sciences 010101 applied mathematics Kinetic equations Besov space Cutoff Initial value problem 0101 mathematics Mathematics::Representation Theory Analysis Smoothing Mathematics |
| Zdroj: | Journal of Differential Equations. 269:1117-1171 |
| ISSN: | 0022-0396 |
| DOI: | 10.1016/j.jde.2019.12.025 |
| Popis: | In this work, we investigate the Cauchy problem for the spatially inhomogeneous non-cutoff Kac equation. If the initial datum belongs to the spatially critical Besov space, we can prove the well-posedness of weak solution under a perturbation framework. Furthermore, it is shown that the solution enjoys Gelfand-Shilov regularizing properties with respect to the velocity variable and Gevrey regularizing properties with respect to the position variable. In comparison with the recent result in [18] , the Gelfand-Shilov regularity index is improved to be optimal. To the best of our knowledge, our work is the first one that exhibits smoothing effect for the kinetic equation in Besov spaces. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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