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

2024/02/09 by Borsoni, Thomas, Lods, Bertrand
#Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2402.06807

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-ε L^∞ bound on the solutions.

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