Communications in Mathematical Sciences
Volume 19 (2021)
On the gradient flow structure of the isotropic Landau equation
Pages: 2319 – 2333
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.
isotropic Landau equation, nonlocal mobility, gradient flow
2010 Mathematics Subject Classification
J.A. is supported by the Joe Oliger Fellowship from Stanford University. The work of L.Y. is partially supported by the National Science Foundation under award DMS-1818449.
Received 4 December 2019
Accepted 3 June 2021
Published 7 October 2021