Applied PDE Group
Nonlinear Partial Differential Equations in Fluid and Solid Mechanics

LT2017b

From gas dynamics with large friction to gradient flows describing diffusion theories

​C. Lattanzio, A.E. Tzavaras, From gas dynamics with large friction to gradient flows describing diffusion theories, Communications in Partial Differential Equations, 42(2), 261-290, 2017
C. Lattanzio, A.E. Tzavaras
gradient flows, Wasserstein distance
2016

We study the emergence of gradient flows in Wasserstein distance as high friction limits of an abstract Euler flow generated by an energy functional. We develop a relative energy calculation that connects the Euler flow to the gradient flow in the diffusive limit regime. We apply this approach to prove convergence from the Euler-Poisson system with friction to the Keller-Segel system in the regime that the latter has smooth solutions. The same methodology is used to establish convergence from the Euler-Korteweg theory with monotone pressure laws to the Cahn-Hilliard equation.