Please use this identifier to cite or link to this item:
http://hdl.handle.net/10397/105951
Title: | De Giorgi argument for weighted L2∩ L∞ solutions to the non-cutoff Boltzmann equation | Authors: | Alonso, R Morimoto, Y Sun, W Yang, T |
Issue Date: | Feb-2023 | Source: | Journal of statistical physics, Feb. 2023, v. 190, no. 2, 38 | Abstract: | This paper gives an affirmative answer to the question of the global existence of Boltzmann equations without angular cutoff in the L∞-setting. In particular, we show that when the initial data is close to equilibrium and the perturbation is small in L2∩ L∞ with a polynomial decay tail, the Boltzmann equation has a unique global solution in the weighted L2∩ L∞-space. In order to overcome the difficulties arising from the singular cross-section and the low regularity, a De Giorgi type argument is crafted in the kinetic context with the help of the averaging lemma. More specifically, we use a strong averaging lemma to obtain suitable Lp-estimates for level-set functions. These estimates are crucial for constructing an appropriate energy functional to carry out the De Giorgi argument. Similar as in Alonso et al. (Rev Mat Iberoam, 2020), we extend local solutions to global ones by using the spectral gap of the linearised Boltzmann operator. The convergence to the equilibrium state is then obtained as a byproduct with relaxations shown in both L2 and L∞-spaces. | Keywords: | De Giorgi argument Level-set estimates Spectral gap Velocity averaging lemma |
Publisher: | Springer New York LLC | Journal: | Journal of statistical physics | ISSN: | 0022-4715 | EISSN: | 1572-9613 | DOI: | 10.1007/s10955-022-03053-8 | Rights: | © The Author(s) 2022 This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. The following publication Alonso, R., Morimoto, Y., Sun, W. et al. De Giorgi Argument for Weighted L2∩ L∞ Solutions to the Non-cutoff Boltzmann Equation. J Stat Phys 190, 38 (2023) is available at https://doi.org/10.1007/s10955-022-03053-8. |
Appears in Collections: | Journal/Magazine Article |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
s10955-022-03053-8.pdf | 1.45 MB | Adobe PDF | View/Open |
Page views
14
Citations as of Jun 30, 2024
Downloads
4
Citations as of Jun 30, 2024
SCOPUSTM
Citations
3
Citations as of Jul 4, 2024
WEB OF SCIENCETM
Citations
3
Citations as of Jul 4, 2024
Google ScholarTM
Check
Altmetric
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.