Boltzmann to Landau from the Gradient Flow Perspective

Abstract

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 $\Gamma$-convergence of gradient flows technique introduced by Sandier and Serfaty. 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.

41.5 pages without references, 4 figures. Comparisons with other weak solutions have been expanded. Typos fixed and more clarifications added. Accepted version. Comments welcome!

References in corpus (1)

• On the uniqueness for the spatially homogeneous Boltzmann equation with a strong angular singularity

Cited by in corpus (1)

• Random batch particle methods for the homogeneous Landau equation