The Landau equation with moderate soft potentials: An approach using ε-Poincaré inequality and Lorentz spaces

This document presents an elementary approach using ε-Poincaré inequality to prove generation of Lp-bounds, p∈(1,∞), for the homogeneous Landau equation with moderate soft potentials γ∈[−2,0). The critical case γ=−2 uses an interpolation approach in the realm of Lorentz spaces and entropy. Alternatively, a direct approach using the Hardy-Littlewood-Sobolev (HLS) inequality and entropy is also presented. On this basis, the generation of pointwise bounds p=∞ is deduced from a De Giorgi argument.