Brenier–Schrödinger problem on compact manifolds with boundary. Issue 3 (4th May 2022)

• Record Type: Journal Article
• Authors: García-Zelada, David; Huguet, Baptiste
• Is Part Of: Stochastic analysis and applications. Volume 40:Issue 3(2022)
• Page Start: 426
• Page End: 454
• Publication Date: 2022-05-04
• Subjects: Brenier–Schrödinger -- entropy -- manifold with boundary -- reflected Brownian motion -- Navier–Stokes equations; 28D20 -- 49Q20 -- 49S05 -- 60G99 -- 76D03 -- 58J65 -- 60J55; Stochastic analysis -- Periodicals; 519.2205
• DOI: 10.1080/07362994.2021.1922292
• Languages: English
• ISSNs: 0736-2994

Abstract

ABSTRACT: 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. Moreover, by a method of taking quotients by reflection groups, we enhance the class of models for which the problem admits a unique solution.