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This paper has been withdrawn by the author due to essential mistakes in some previous versions.

This paper has been withdrawn by the author due to the unsure solution to the Dyson-Schwinger equation.

This paper has been withdrawn due to a crucial theoretical and experimental error.

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This paper has been withdrawn by the author due to a crucial sign error in equation 1.

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In this paper, we give a sufficient condition to guarantee the existence of a smooth solution of the Navier-Stokes Equation with the nice decreasing properties at infinity. In this way, we prove the existence of smooth physically reasonable…

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This paper has been withdrawn.

In this paper we describe a method to derive classical solutions of the Navier-Stokes equations for non-stationary initial value problems in domain R^n (n = 2, 3 or higher). A new closed-form analytic solution of the incompressible…

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In this paper we describe a method to derive solutions of the incompressible Navier- Stokes system of equations for non-stationary initial value problems in $\mathbb{R}^n$. We show that for a given smooth solenoidal initial velocity vector…

This paper has been withdrawn by the authors, due to inappropriate discussions in Discussions.

There are few approaches to the solution of a system of nonlinear differential equations in partial derivatives, for example $\cite{NK87} - \cite{EK98}$. In our paper we propose an approach that was used to solve the Navier-Stokes equations…

This paper has been withdrawn by the author due to need for more improvement.

This paper has been withdrawn by the authors, due to a crucial error.

A few basic, intuitive, properties of the Navier-Stokes system of equations for incompressible fluid flows are discussed in this paper. We present a rephrased interpretation of the Navier-Stokes equation in a space having an arbitrary…

This paper has been withdrawn.