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arXiv · 1601.05966

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

Corrado Lattanzio·Athanasios E. Tzavaras
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Abstract

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.

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Corrado Lattanzio, Athanasios E. Tzavaras. 2016-01-22. From gas dynamics with large friction to gradient flows describing diffusion theories. https://doi.org/10.1080/03605302.2016.1269808

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