On the gradient flow structure of the isotropic Landau equation

2019/12/05 by Jing An, Lexing Ying, An, Jing +1
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1912.02343

openalex publication_date 2019/12/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the isotropic Landau equation equipped with the Coulomb potential introduced by Krieger-Strain and Gualdani-Guillen can be identified with the gradient flow of the entropy in the probability space with respect to a Riemannian metric tensor with nonlocal mobility. We give characterizations of the corresponding geodesics equations and present a convergence rate result by estimating its Hessian operator.

Citations

• A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem

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