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math.AP2026
Nonlinear kinetic Fokker-Planck equations as gradient flows of the free energy
Giovanni Brigati, Guillaume Carlier, Jean Dolbeault +1
We consider nonhomogeneous kinetic equations that involve a free transport operator and a diffusion of porous medium type acting on velocities. The main novelty is a gradient flow…
math.AP2026
The fundamental solution of a nonlinear kinetic Fokker-Planck equation
Giovanni Brigati, Guillaume Carlier, Jean Dolbeault
This paper is devoted to a fundamental solution of a nonlinear kinetic equation involving a porous medium or fast diffusion operator acting on velocities. Such a nonlinearity has i…
math.AP2024
Well-posedness and convergence of entropic approximation of semi-geostrophic equations
Guillaume Carlier, Hugo Malamut
We prove existence and uniqueness of solutions for an entropic version of the semi-geostrophic equations. We also establish convergence to a weak solution of the semi-geostrophic e…