Year: 2024
Author: Chuqi Cao, Renjun Duan, Zongguang Li
Communications in Mathematical Analysis and Applications, Vol. 3 (2024), Iss. 1 : pp. 61–120
Abstract
In this paper, we consider the perturbed solutions with polynomial tail in large velocities for the non-cutoff Boltzmann equation near global Maxwellians in the whole space. The global in time existence is proved in the weighted Sobolev spaces and the almost optimal time decay is obtained in Fourier transform based low-regularity spaces. The result shows a time-velocity decay structure of solutions that can be decomposed into two parts. One part allows the slow polynomial tail in large velocities, carries the initial data and enjoys the exponential or arbitrarily large polynomial time decay. The other part, with zero initial data, is dominated by the non-negative definite symmetric dissipation and has the exponential velocity decay but only the slow polynomial time decay.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cmaa.2024-0003
Communications in Mathematical Analysis and Applications, Vol. 3 (2024), Iss. 1 : pp. 61–120
Published online: 2024-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 60
Keywords: Boltzmann equation angular non-cutoff large time behavior.