Euler and Navier–Stokes Equations as Self-Consistent Fields

V. V. Vedenyapin^a^,^b^,*, A. A. Andreeva^c^,**, and V. V. Vorobyeva^c^,***
Translated by I. Ruzanova

^aKeldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow, 125047 Russia

^bRUDN University, Moscow, 117198 Russia

^cMoscow Institute of Physics and Technology (State University), Dolgoprudnyi, Moscow oblast, 141700 Russia

Correspondence to: *e-mail: vicveden@yahoo.com
Correspondence to: **e-mail: nurka.de@yandex.ru
Correspondence to: ***e-mail: vvorobyeva@yandex.ru

Received 1 February, 2018

Abstract—New kinetic equations are proposed from which the incompressible Euler and Navier–Stokes equations are derived by making an exact substitution. A class of exact solutions of the Navier–Stokes equation and the form of singularities for a gradient catastrophe are obtained.

DOI: 10.1134/S1064562418030171