Open Access
2016 Existence and Smoothness of the Navier-Stokes Equation in Two and Three-Dimensional Euclidean Space
Tim Tarver
Author Affiliations +
J. Phys. Math. 7(2): 1-7 (2016). DOI: 10.4172/2090-0902.1000167

Abstract

A solution to this problem has been unknown for years and the fact that it hasn’t been solved yet leaves a lot of unanswered questions regarding Engineering and Pure Mathematics. Turbulence is a specific topic in fluid mechanics which is a vital part of the course when it comes to real life situations. In two and three dimensional systems of equations and some initial conditions, if the smooth solutions exist, they have bounded kinetic energy. In three space dimensions and time, given an initial velocity vector, there exists a velocity field and scalar pressure field which are both smooth and globally defined that solve the Navier-Stokes equations. There are difficulties in two-dimensions and three dimensions in a possible solution and which have been unsolved for a long time and our goal is to propose a solution in three-dimensions. Lets see if we can relate a couple of courses of pure mathematics to come up with an implication.

Citation

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Tim Tarver. "Existence and Smoothness of the Navier-Stokes Equation in Two and Three-Dimensional Euclidean Space." J. Phys. Math. 7 (2) 1 - 7, 2016. https://doi.org/10.4172/2090-0902.1000167

Information

Published: 2016
First available in Project Euclid: 31 August 2017

Digital Object Identifier: 10.4172/2090-0902.1000167

Keywords: Navier-Stokes equation , three-dimensional Euclidean space

Rights: Copyright © 2016 Ashdin Publishing (2009-2013) / OMICS International (2014-2016)

Vol.7 • No. 2 • 2016
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