On The Solution Of The 4th Clay Millenium problem about the Navier-Stokes Equations. Equivalence of smooth compact support and smooth Schwartz, initial conditions
|Main Author:||Kyritsis, Constantinos|
1st INTERNATIONAL CONFERENCE ON QUANTITATIVE, SOCIAL, BIOMEDICAL AND ECONOMIC ISSUES 2017 - ICQSBEI 2017
In this paper I prove, using some relatively recent ideas suggested by T. Tao , that the Schwartz initial conditions of the its official formulation of the problem in the direction of regularity are equivalent to the simpler compact support initial conditions. I prove also, using the Helmholtz-Hodge orthogonal decomposition of vector fields, a powerful fundamental decomposition of the Euler and Navier-Stokes equations which is significant for the internal symmetries of the equations.