2021/01/01 by Shuzhe Cai, Cai, Shuzhe
Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #Cold Atom Physics and Bose-Einstein Condensates #FOS: Mathematics #FOS: Physical sciences #Gas Dynamics and Kinetic Theory #Mathematical Physics (math-ph) #Optical properties and cooling technologies in crystalline materials
paper · pdf · doi:10.48550/arxiv.2101.00144
openalex publication_date 2021/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The paper is concerned with the spatially homogeneous isotropic Boltzmann equation for Bose-Einstein particles with quantum collision kernel where the interaction potential ϕ(\bf x) can be approximately written as the delta function plus a certain attractive potential such that the Fourier transform \widehatϕ of ϕ behaves like 0 ≤ \widehatϕ(ξ) ≤ \rm const. |ξ|η for |ξ|<<1 for some constant η≥ 1. We prove that in this case, there is no condensation in finite time for all temperatures and all solutions, and thus it is completely different from the case \widehatϕ(ξ) ≥ \rm const.|ξ|η for |ξ|<<1 with 0≤ η<1/4 as considered in \citeCai-Lu. For a class of initial data that have some nice integrability near the origin, we also get some regularity, stability and L∞ estimate.