Generalized Brenier Principle and the Closure Problem of Landgren–Monin–Novikov Hierarchy for Vorticity Field

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详细

Brenier’s concept – a representation of solutions to the equations of ideal incompressible fluids in terms of probability measures on the set of Lagrangian trajectories in the case of their stochasticity, is a generalization of Arnold’s principle of least action of finding smooth solutions of Euler’s equations. In this work, the variational generalized Brenier principle (Brenier, J. Am. Math. Soc. 1989) is used to close the infinite chain of Landgren–Monin–Novikov equations for the n-point probability density functions fn of the vortex field of two-dimensional turbulence. In addition, within the framework of the statistical approach, an approximation of the variational problem with conditions at the ends posed by Shnirelman (Mat. Sat. 1985) for the Euler equation is proposed.

作者简介

V. Grebenev

Federal Research Center for Information and Computational Technologies

编辑信件的主要联系方式.
Email: vngrebenev@gmail.com
俄罗斯联邦, Novosibirsk

A. Grishkov

University of Sao Paulo

Email: grishkov@ime.usp.br
巴西, Sao Paulo

参考

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