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arXiv · 2601.03107

On the monotonicity of the entropy production in the Landau-Maxwell equation

Côme Tabary
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Abstract

We study the homogeneous Landau equation with Maxwell molecules and prove that the entropy production is non-increasing when the directional temperatures are well-distributed. It implies that for any initial condition with finite mass and energy, the entropy production is guaranteed to be non-increasing after a certain explicit time. We also obtain exponential decay of the entropy production. We provide an explicit formula for the derivative of the entropy production which may be a starting point for future progress towards full monotonicity.

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Côme Tabary. 2026-01-06. On the monotonicity of the entropy production in the Landau-Maxwell equation. https://arxiv.org/abs/2601.03107

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