On the solution of the 4th clay millennium problem. Proof of the regularity of the solutions of the Euler and Navier-Stokes equations, based on the conservation of particles as a local structure of the fluid, formulated in the context of continuous fluid mechanics.

Main Author: Kyritsis, Constantinos
Format: Article
Language: English
Published: 2017
Online Access: http://cris.teiep.gr/jspui/handle/123456789/1575
Physical Description: p.p. 26
Abstract: As more and more researchers tend to believe that with the hypotheses of the official formulation of the 4th Clay Millennium problem a blowup may occur, a new goal is set: to find the simplest and most physically natural enhancement of the hypotheses in the official formulation so that the regularity can be proved in the case of 3 dimensions too. The position of this paper is that the standard assumptions of the official formulation of the 4th Clay millennium problem, although they reflect, the finiteness and the conservation of momentum and energy and the smoothness of the incompressible physical flows, they do not reflect the conservation of particles as local structure. By formulating the later conservation and adding it to the hypotheses, we prove the regularity (global in time existence and smoothness) both for the Euler and the Navier-Stokes equations.