From gas dynamics with large friction to gradient flows describing diffusion theories
Online Publication Date2016-12-12
Print Publication Date2017-02
Permanent link to this recordhttp://hdl.handle.net/10754/603947
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AbstractWe 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.
CitationLattanzio, C., & Tzavaras, A. E. (2016). From gas dynamics with large friction to gradient flows describing diffusion theories. Communications in Partial Differential Equations, 42(2), 261–290. doi:10.1080/03605302.2016.1269808
SponsorsAET was supported by funding from King Abdullah University of Science and Technology (KAUST).
PublisherInforma UK Limited