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arXiv · 2402.06807

Quantitative relaxation towards equilibrium for solutions to the Boltzmann-Fermi-Dirac equation with cutoff hard potentials

Thomas Borsoni·Bertrand Lods
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Abstract

We provide the first quantitative result of convergence to equilibrium in the context of the spatially homogeneous Boltzmann-Fermi-Dirac equation associated to hard potentials interactions under angular cut-off assumption, providing an explicit - algebraic - rate of convergence to Fermi-Dirac steady solutions. This result complements the quantitative convergence result of Liu and Lu and is based upon new uniform-in-time-and-$\varepsilon$ $L^{\infty}$ bound on the solutions.

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Thomas Borsoni, Bertrand Lods. 2024-02-09. Quantitative relaxation towards equilibrium for solutions to the Boltzmann-Fermi-Dirac equation with cutoff hard potentials. https://arxiv.org/abs/2402.06807

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