Entropic regularisation of non-gradient systems

Daniel Adams, Manh Hong Duong, Goncalo dos Reis

Published 2021-04-09Version 1

The theory of (Wasserstein) gradient flows in the space of probability measures has made enormous progress over the last twenty years. Nonetheless, many partial differential equations (PDEs) of interest do not have gradient flow structure and, a priori, the theory is not applicable. In this paper, we develop a time-discrete entropic regularised variational scheme for a general class of such non-gradient PDEs. We prove the convergence of the scheme and illustrate the breadth of the proposed framework with concrete examples including the non-linear kinetic Fokker-Planck (Kramers) equation and a nonlinear degenerate diffusion of Kolmogorov type.