Journée groupe de contact FNRS ULB-UCLouvain (Analysis and PDEs)

by Alice Marveggio (Institute for Applied Mathematics, Bonn), Jonathan Junné (Delft Institute of Applied Mathematics, Delft)

Thursday 11 Dec 2025, 12:00 → 17:00 Europe/Brussels

B/2nd floor-B.203 - Seminar room (Marc de Hemptinne (chemin du Cyclotron, 2, Louvain-la-Neuve))

12h-14h30 - Lunch with speakers
 

14h30 - Alice Marveggio (Institute for Applied Mathematics, Bonn): The Verigin problem with phase transition as Wasserstein flow 

We study the modeling of a compressible two-phase flow in a porous medium.

The governing PDE system is known as the Verigin problem with phase transition, which is the compressible analog to the Muskat problem. 

Our aim is to prove the convergence of an implicit time discretization scheme using the Wasserstein distance, obtaining distributional solutions in the limit that satisfy an optimal energy-dissipation rate.

This talk is based on a joint work with Anna Kubin and Tim Laux.

15h30 - Coffee break

16h -  Jonathan Junné (Delft Institute of Applied Mathematics, Delft): Improved stability estimates for the Vlasov-Poisson system 

We review recent developments on stability estimates for the Vlasov-Poisson (VP) system and variants thereof. In his seminal work of 2006, Loeper [1] proved  the uniqueness of weak solutions for VP using optimal transport.

Although his argument ensures uniqueness, the resulting stability estimate is not optimal. This limitation was overcome in 2017 by Iacobelli [2], who introduced the kinetic Wasserstein distance, a nonlinear modification of the classical Wasserstein distance that captures the anisotropy between position and momentum variables and yields improved stability estimates.

After outlining this method, we discuss some variants of (VP) for which optimal stability estimates can be deduced through the kinetic Wasserstein distance.

[1] Loeper, Grégoire. "Uniqueness of the solution to the Vlasov–Poisson system with bounded density." Journal de mathématiques pures et appliquées 86.1 (2006): 68-79.

[2] Iacobelli, Mikaela. "A new perspective on Wasserstein distances for kinetic problems." Archive for Rational Mechanics and Analysis 244.1 (2022): 27-50.