arXiv Probability
arXiv Probability
5 years ago

Small noise limit and convexity for generalized incompressible flows, Schr\"odinger problems, and optimal transport. (arXiv:1810.12036v2 [math.AP] UPDATED)

Aymeric Baradat, Léonard Monsaingeon
This paper is concerned with six variational problems and their mutual connections: The quadratic Monge-Kantorovich optimal transport, the Schr\"odinger problem, Brenier's relaxed model for incompressible fluids, the so-called Br\"odinger problem recently introduced by M. Arnaudon & al. [3], the multiphase Brenier model, and the multiphase Br\"odinger problem. All of them involve the minimization of a kinetic action and/or a relative entropy of some path measures with respect to the reversible Brownian motion. As the viscosity parameter $\nu\to 0$ we establish Gamma-convergence relations between the corresponding problems, and prove the convergence of the associated pressures arising from the incompressibility constraints. We also present new results on the time-convexity of the entropy for some of the dynamical interpolations. Along the way we extend previous results by H. Lavenant [30] and J-D. Benamou & al. [10].

Publisher URL: http://arxiv.org/abs/1810.12036

DOI: arXiv:1810.12036v2

You might also like
Discover & Discuss Important Research

Keeping up-to-date with research can feel impossible, with papers being published faster than you'll ever be able to read them. That's where Researcher comes in: we're simplifying discovery and making important discussions happen. With over 19,000 sources, including peer-reviewed journals, preprints, blogs, universities, podcasts and Live events across 10 research areas, you'll never miss what's important to you. It's like social media, but better. Oh, and we should mention - it's free.

  • Download from Google Play
  • Download from App Store
  • Download from AppInChina

Researcher displays publicly available abstracts and doesn’t host any full article content. If the content is open access, we will direct clicks from the abstracts to the publisher website and display the PDF copy on our platform. Clicks to view the full text will be directed to the publisher website, where only users with subscriptions or access through their institution are able to view the full article.