On the convergence of soft potential dynamics to hard sphere dynamics

DOI10.3233/ASY-171448zbMATH Open1395.82157arXiv1601.04182OpenAlexW2963651031MaRDI QIDQ4575571

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Publication date: 13 July 2018

Published in: Asymptotic Analysis (Search for Journal in Brave)

Abstract: We address a question raised in the work of Gallagher, Saint-Raymond and Texier (From Newton to Boltzmann: Hard Spheres and Short-range Potentials, Z"urich Lectures in Advanced Mathematics, EMS, 2013) that concerns the convergence of soft-potential dynamics to hard sphere dynamics. In the case of two particles, we establish that hard sphere dynamics is the limit of soft sphere dynamics in the weak-star topology of BV. We view our result as establishing a topological method by which to construct weak solutions to the ODE of hard sphere motion.

Full work available at URL: https://arxiv.org/abs/1601.04182

zbMATH Keywords

weak solutionsBoltzmann equationhard sphereskinetic theoryhard particle dynamics

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