In this study, the Navier-Stokes equations’ 4th Clay Millennium issue is solved in the direction of regularity. It accomplishes this by relying on the hypothesis of limiting beginning energy. The pressures are bounded in small time intervals, as demonstrated by projecting the bounded by the conservation of energy, virtual work of the pressures forces on specifically chosen bundles of instantaneous routes, which is the final important finding to deduce the regularity. It is shown that there is no Blow-up not just in finite time, but also at T=+.

**Author (S) Details**

**Konstantinos E. Kyritsis**

Department of Accounting-Finance, Psathaki Preveza 48100, University of Ioannina, Greece.

View Book :- https://stm.bookpi.org/NVST-V6/article/view/4134