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

Organisé par

Institut Henri Poincaré

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 l

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