B. Huguet: Brenier-Schrödinger problem : a probabilistic approach to Navier-Stokes equations

The Brenier problem is a variational approach of Euler equations whose solutions are path measures, minimising the kinetic energy. Using an appropriate notion of energy, this approach can be extended to different fluid evolution models. In particular, the Nelson (or mean velocity) kinetic energy links Navier-Stokes equations to the Brenier-Schrödinger problem. This talk will introduce the Brenier-Shrödinger problem on compact manifolds with boundary and explain the link with viscous fluid evolution, especially concerning the impermeability condition. We will also give existence results in compact manifolds with boundary such as rectangles or regular triangles.

Talk given for the Schromoka conference in Lisbon, September 14-17, 2021