2021/02/21 by Salem, Samir
#Analysis of PDEs (math.AP) #FOS: Mathematics
paper · doi:10.48550/arxiv.2102.10667
A quadratic optimal transport metric on the set of probability measure over \R2 is introduced. The quadratic cost is given by the euclidean norm on \R2 associated to some well chosen symmetric positive matrix, which makes the metric equivalent to the usual Wasserstein-2 metric. The dissipation of the distance to the equilibrium along the kinetic Fokker-Planck flow, is bounded by below in terms of the distance itself. It enables to obtain some new type of trend to equilibrium estimate in Wasserstein-2 like metric, in the case of non-convex confinement potential.