  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.
