On the Incompressible Navier-Stokes Equations and the Malliavin Calculus on $G={\rm SDiff}(M)$ -

On the Incompressible Navier-Stokes Equations and the Malliavin Calculus on $G={\rm SDiff}(M)$

Time: 2024-01-22 Published By: He Liu

Speaker(s): Xiang-Dong Li(AMSS-CAS)

Time: 14:00-15:30 January 30, 2024

Venue: Room 77201, Jingchunyuan 78, BICMR

In this talk, I will present a new derivation of the incompressible Navier-Stokes equations on a compact Riemannian manifold $M$ via the Bellman dynamical programming principle on the infinite dimensional group of volume-preserving diffeomorphisms $G={\rm SDiff}(M)$. Moreover, I will propose a probabilistic approach for the regularity issue of the incompressible NS equations by developing the Malliavin calculus on $G={\rm SDiff}(M)$. Joint with Guo-Ping Liu (HUST Wuhan).