2019/10/04 by Samir Salem, Salem, Samir
Computer Science · Engineering · Materials Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Advanced Thermodynamics and Statistical Mechanics #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Gas Dynamics and Kinetic Theory #Material Dynamics and Properties #Mathematical Physics (math-ph) #Nanopore and Nanochannel Transport Studies
paper · pdf · doi:10.48550/arxiv.1910.01883
openalex publication_date 2019/10/04 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28
We derive the 3D spatially homogeneous Boltzmann's equation with moderately\nsoft potentials and singular angular interaction, from an interacting particles\nsystem. The collision kernel is of the form B(z,\σ)=|z|\γb\(\n\(z)/(|z|)\⋅ \σ\) and for K>0,\n\sin(\θ)b\(\cos(\θ)\)\∼ K\θ-1-\ν, with \γ\∈\n(-2,-1) and \ν\∈(1,2) satisfying \γ+\ν>0. We use at the particle\nlevel the regularizing effects of the grazing collisions, in order to control\nthe singularity of the soft potential. This enables to use a classical\ncompactness argument, and provide a qualitative convergence result from the\ninteracting particles system toward the solution of the limit macroscopic\nequation.\n