39 citations · 76 across the 12 of their papers we have counts for
12 papers
Geometry on the Wasserstein space over a compact Riemannian manifold
Hao Ding, Shizan Fang
We will revisit the intrinsic differential geometry of the Wasserstein space over a Riemannian manifold, due to a series of papers by Otto, Villani, Lott, Ambrosio, Gigli, Savaré a…
Vorticity, Helicity, Intrinsinc geometry for Navier-Stokes equations
Shizan Fang, Zhongmin Qian
We will consider the Navier-Stokes equation on a Riemannian manifold M with Ricci tensor bounded below, the involved Laplacian operator is De Rham-Hodge Laplacian. The novelty of t…
Nash embedding, shape operator and Navier-Stokes equation on a Riemannian manifold
Shizan Fang
What is the suitable Laplace operator on vector fields for the Navier-Stokes equation on a Riemannian manifold? In this note, by considering Nash embedding, we will try to elucidat…
Small time asymptotics for Brownian motion with singular drift
Zhen-Qing Chen, Shizan Fang, Tusheng Zhang
We establish a small time large deviation principle and a Varadhan type asymptotics for Brownian motion with singular drift on $\bR^d$ with whose infinitesimal generator…
Generalized stochastic Lagrangian paths for the Navier-Stokes equation
Marc Arnaudon, Ana Bela Cruzeiro, Shizan Fang
In the note added in proof of the seminal paper [Groups of diffeomorphisms andthe motion of an incompressible fluid, Ann. of Math. 92 (1970), 102-163], Ebinand Marsden introduced t…
Remarks on spectral gaps on the Riemannian path space
Shizan Fang, Bo Wu
In this paper, we will give some remarks on links between the spectral gap of the Ornstein-Uhlenbeck operator on the Riemannian path space with lower and upper bounds of the Ricci…