Centre for Mathematics, University of Coimbra

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Type:	Preprint
National /International:	International
Title:	Variational solutions to the abstract Euler equation
Publication Date:	2019-05-15
Authors:	- Dmitry Vorotnikov
Abstract:	We study a class of nonlinear evolutionary equations of a certain structure reminiscent of the incompressible Euler equations. This includes, in particular, the ideal MHD, multidimensional Camassa-Holm, EPDiff, Euler-α and Korteweg-de Vries equations, and two models of incompressible elastodynamics. We interpret the "abstract Euler equation” as a concave maximization problem in the spirit of Y.Brenier. Comm. Math. Phys. (2018) 364(2) 579-605. An optimizer determines a “time- noisy” version of the original unknown function, and the latter one may be retrieved by time-averaging. Assuming a certain “trace condition”, which holds for the above-mentioned examples, we prove the existence of the generalized solutions determined by the maximizers.
Institution:	DMUC 19-15
Online version:	http://www.mat.uc.pt...prints/eng_2019.html
Download:	Not available