A gradient flow approach to the Boltzmann equation

Matthias Erbar

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arXiv · 1603.00540

A gradient flow approach to the Boltzmann equation

Matthias Erbar

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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.

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Matthias Erbar. 2016-03-02. A gradient flow approach to the Boltzmann equation. https://arxiv.org/abs/1603.00540

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