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

2023/08/08 by Ricardo J. Alonso, Alonso, R. J., Véronique Bagland +3
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2308.04384

openalex publication_date 2023/08/08 · openalex created_date 2023/08/18 · openalex updated_date 2026/07/28

Abstract

This document presents an elementary approach using ε-Poincaré inequality to prove generation of L^p-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.

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