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The Wasserstein Distance Between Two Boltzmann Solutions Can Increase

Year: 2026

Type: article

Abstract: For Maxwell molecules, Tanaka proved that the quadratic Wasserstein distance between two solutions of the spatially homogeneous Boltzmann equation never increases. Villani asked whether this remains true for other collision kernels. This paper shows that it does not: for every hard potential with angular cutoff, hard spheres included, there are smooth initial data for which the distance strictly increases. The proof is analytic and rests on an explicit Kantorovich dual certificate. LaTeX source, figure and PDF.

Source: Zenodo (CERN European Organization for Nuclear Research)

DOI: 10.5281/zenodo.24128011

Author: Bhattacharjee, Deep

Language: English

Topic: Gas Dynamics and Kinetic Theory

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7225834138

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