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This paper was withdrawn by the author.

Regularity properties of strong solutions are considered.

In this paper we propose new method for proving of global solutions for 3D Navier-Stokes equations. This complies an application to the Clay Institute Millennium Prize Navier Stokes Problem. The proposed method can be applied for…

This paper has been withdrawn by the author, due to a crucial error in the proof of Thm.1

This paper has been withdrawn by the author, due to a significant error in section 4.3.1.

We prove global smooth continuation for smooth finite-energy solutions of the three-dimensional incompressible Navier--Stokes equations by a two-part first-threshold argument. Part I proves the axisymmetric-with-swirl theorem in the exact…

This paper has been withdrawn by the author.

In this paper, we prove existence of smooth solutions of the Navier-Stokes equations that gives a positive answer to the problem proposed by Fefferman [3].

This paper has been withdrawn by the author, due an error in claim 1.

This paper has been withdrawn.