A gradient flow approach to the Boltzmann equation
Matthias Erbar
Universität Bielefeld, Germany
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Abstract
We show that the spatially homogeneous Boltzmann equation evolves as the gradient flow of the entropy with respect to a suitable geometry on the space of probability measures which takes the collision process into account. This gradient flow structure allows to give a new proof for the convergence of Kac’s random walk to the homogeneous Boltzmann equation, exploiting the stability of gradient flows.
Cite this article
Matthias Erbar, A gradient flow approach to the Boltzmann equation. J. Eur. Math. Soc. (2023), published online first
DOI 10.4171/JEMS/1349