A solution of the 4th clay millennium problem about the Navier-Stokes equations.

Main Author: Kyritsis, Konstantinos
Format: Article
Language: English
Published: Preprint TEI OF EPIRUS 2018
Subjects:
Online Access: http://cris.teiep.gr/jspui/handle/123456789/1628
id cris-123456789-1628
recordtype dspacecris
spelling cris-123456789-16282018-02-28T01:00:28Z A solution of the 4th clay millennium problem about the Navier-Stokes equations. Kyritsis, Konstantinos Mathematics Incompressible flows Navier-Stokes equations 4th Clay millennium problem In this paper it is solved the 4th Clay Millennium problem about the Navier-Stokes equations, in the direction of regularity. It is done so by utilizing the hypothesis of finite initial energy and by applying the regularity of the Poisson equation which is a well- studied linear PDE, involving the also well studies harmonic functions. The Poisson equation either in scalar or vector form, relates many magnitudes of the flow, like pressures and velocities, velocity and vorticity and velocities and viscosity forces. It is also proved 5 new necessary and sufficient conditions of regularity based on the pressures, viscosity forces, trajectories lengths, pressure forces etc. The final key result to derive the regularity is that the pressures are bounded in finite time intervals, as proved after projecting the work of the pressures forces on specially chosen bundles of paths. 2018-02-25 Άρθρο http://cris.teiep.gr/jspui/handle/123456789/1628 en 26 Preprint TEI OF EPIRUS Preveza, Greece
institution T.E.I. of Epirus
collection DSpace CRIS
language English
topic Mathematics
Incompressible flows
Navier-Stokes equations
4th Clay millennium problem
spellingShingle Mathematics
Incompressible flows
Navier-Stokes equations
4th Clay millennium problem
Kyritsis, Konstantinos
A solution of the 4th clay millennium problem about the Navier-Stokes equations.
abstract In this paper it is solved the 4th Clay Millennium problem about the Navier-Stokes equations, in the direction of regularity. It is done so by utilizing the hypothesis of finite initial energy and by applying the regularity of the Poisson equation which is a well- studied linear PDE, involving the also well studies harmonic functions. The Poisson equation either in scalar or vector form, relates many magnitudes of the flow, like pressures and velocities, velocity and vorticity and velocities and viscosity forces. It is also proved 5 new necessary and sufficient conditions of regularity based on the pressures, viscosity forces, trajectories lengths, pressure forces etc. The final key result to derive the regularity is that the pressures are bounded in finite time intervals, as proved after projecting the work of the pressures forces on specially chosen bundles of paths.
format Άρθρο
author Kyritsis, Konstantinos
author-letter Kyritsis, Konstantinos
title A solution of the 4th clay millennium problem about the Navier-Stokes equations.
title_short A solution of the 4th clay millennium problem about the Navier-Stokes equations.
title_full A solution of the 4th clay millennium problem about the Navier-Stokes equations.
title_fullStr A solution of the 4th clay millennium problem about the Navier-Stokes equations.
title_full_unstemmed A solution of the 4th clay millennium problem about the Navier-Stokes equations.
title_sort solution of the 4th clay millennium problem about the navier-stokes equations.
publisher Preprint TEI OF EPIRUS
publisherplace Preveza, Greece
publishDate 2018
url http://cris.teiep.gr/jspui/handle/123456789/1628
physical 26
_version_ 1646089698406301696
score 11.370737