On the Convergence of Soft Potential Dynamics to Hard Sphere Dynamics

2016/01/16 by Mark Wilkinson, Wilkinson, Mark
Mathematics · Physics and Astronomy · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.CA #math.MP

paper · pdf · doi:10.48550/arxiv.1601.04182

25 pages

arxiv created 2016/01/16 · arxiv updated 2016/01/19

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, Zürich 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.

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