Long-time convergence of Wasserstein gradient flows of (flat-)convex energies with diffusion

par FILIPPO SANTAMBROGIO (Institut Camille Jordan, UCBL)

mercredi 23 sept. 2026, 10:00 → 12:00 Europe/Paris

I will present the main ideas contained in the paper https://arxiv.org/abs/2507.12385, which provides rates of convergence to the minimizer for parabolic PDEs which are W_2 gradient flow of energies of the form F(ρ)+ε E(ρ), where F is a convex functional on probability measures satisfying some extra assumptions, and E is the classical entropy E(ρ)=\int ρ log ρ. In particular, the PDE includes a linear diffusion term. The proof is based on comparisons between the "flat" (L^2) and Wasserstein slopes thanks to suitable functional inequalities, and requires to prove that some bounds on the density ρ_t are preserved along the evolution.