On the 4th Clay Millennium Problem for the Periodic Navier Stokes Equations

Abstract

A rigorous proof of no finite time blowup of the 3D Incompressible Navier Stokes equations in R³/Z³ is hereby shown using Geometric Algebra and subsequently the Gagliardo-Nirenberg and Pr kopa-Leindler inequalities are used to prove that the integrand of the integral form of the solution obtained can be set to zero everywhere in space and time, as well as results on the velocity-pressure distribution using Debreu's, Brouwer's, Lusin's and a final theorem proving no blowup on [0,\(\infty\)]. A complex equation's values for positive and t tending to large values indicates with the help of five theorems that as  approaches positive infinity,  approaches infinity.