Boltzmann to Landau from the gradient flow perspective

We revisit the grazing collision limit connecting the Boltzmann equation to the Landau(-Fokker–Planck) equation from their recent reinterpretations as gradient flows. Our results are in the same spirit as the Γ-convergence of gradient flows technique introduced by Sandier and Serfaty [39]; Serfaty [41]. In this setting, the grazing collision limit reduces to showing the lower semi-continuous convergence of the Boltzmann entropy-dissipation to the Landau entropy-dissipation.