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math.PR2025
-entropy formulas and Langevin deformation on the -Wasserstein space over Riemannian manifolds
Rong Lei, Xiang-Dong Li, Yu-Zhao Wang
We first prove the -entropy formula and rigidity theorem for the geodesic flow on the -Wasserstein space over a complete Riemannian manifold with bounded geometry condition…
math.PR2025
On the Navier-Stokes equations and the Hamilton-Jacobi-Bellman equation on the group of volume preserving diffeomorphisms
Xiang-Dong Li, Guoping Liu
In this paper, we give a new derivation of the incompressible Navier-Stokes equations on a compact Riemannian manifold via the Bellman dynamic programming principle on the infi…
math.PR2024
Langevin deformation for Rényi entropy on Wasserstein space over Riemannian manifolds
Rong Lei, Songzi Li, Xiang-Dong Li
We introduce the Langevin deformation for the Rényi entropy on the -Wasserstein space over or a Riemannian manifold, which interpolates between the porous medi…