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SUMMARY:Long-time convergence of Wasserstein gradient flows of (flat-)conv
 ex energies with diffusion
DTSTART:20260923T080000Z
DTEND:20260923T100000Z
DTSTAMP:20261010T191100Z
UID:indico-event-17358@indico.math.cnrs.fr
DESCRIPTION:Speakers: FILIPPO SANTAMBROGIO (Institut Camille Jordan\, UCBL
 )\n\nI will present the main ideas contained in the paper https://arxiv.o
 rg/abs/2507.12385\, which provides rates of convergence to the minimizer f
 or 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 satisf
 ying 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 p
 roof is based on comparisons between the "flat" (L^2) and Wasserstein slop
 es thanks to suitable functional inequalities\, and requires to prove that
  some bounds on the density ρ_t are preserved along the evolution. \n\nh
 ttps://indico.math.cnrs.fr/event/17358/
URL:https://indico.math.cnrs.fr/event/17358/
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