Existence and Smoothness of the Navier-Stokes Equation in Two and Three-Dimensional Euclidean Space
Department of Mathematics, Bethune-Cookman University, USA
- *Corresponding Author:
- Tim Tarver
Professor, Department of Mathematics
Bethune-Cookman University, USA
E-mail: [email protected]il.com
Received date: January 20, 2016; Accepted date: May 02, 2016; Published date: May 06,2016
Citation: Tarver T (2016) Existence and Smoothness of the Navier-Stokes Equation in Two and Three-Dimensional Euclidean Space. J Phys Math 7: 167. doi:10.4172/2090-0902.1000167
Copyright: © 2016 Tarver T. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
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.