Brenier-Schrödinger problem on compact manifold with boundary

David García-Zelada (1, 2) , Baptiste Nicolas Huguet (3)

1 I2M - Institut de Mathématiques de Marseille
2 LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation
3 IMB - Institut de Mathématiques de Bordeaux

We consider the Brenier-Schrödinger problem on compact manifolds with boundary. In the spirit of a work by Arnaudon, Cruzeiro, Léonard and Zambrini, we study the kinetic property of regular solutions and obtain a link to the Navier-Stokes equations with an impermeability condition. We also enhance the class of models for which the problem admits a unique solution. This involves a method of taking quotients by reflection groups for which we give several examples.

Mots clés: Brenier-Schrödinger; entropy; manifold with boundary; reflected Brownian motion; Navier-Stokes equations

Domaines: Probabilités [math.PR]

David García-Zelada, Baptiste Nicolas Huguet. Brenier-Schrödinger problem on compact manifold with boundary. Stochastic Analysis and Applications, 2021, 40 (3). ⟨hal-03140519⟩