Global solutions in W_k^ζ,pL^∞_TL²_v for the Boltzmann equation without cutoff

2020/08/24 by Haoyu Zhang, Zhang, Haoyu
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2008.10269

openalex publication_date 2020/08/24 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

The Boltzmann equation without an angular cutoff in a three-dimensional periodic domain is considered. The global-in-time existence of solutions in a function space W_k^ζ,pL^∞_TL²_v with p>1 and ζ>3(1-(1)/(p)) is established in the perturbation framework and the long-time behavior of solutions is also obtained for both hard and soft potentials. The proof is based on several norm estimates.

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