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2017•arXiv (Cornell University)Open access

On existence of the incompressible Navier-Stokes equation and the Euler equation

Yanyou Qiao

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Abstract

In this paper, we suggest a possible series form solution to the Navier-Stokes equation and the Euler equation. With the initial velocity vector known, a series form solution for the velocity vector and pressure can be calculated. We admit that the convergence of these series still need to be proved before completely solving the existence of the Navier-Stokes equation and the Euler equation.

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What this paper is about

In this paper, we suggest a possible series form solution to the Navier-Stokes equation and the Euler equation. With the initial velocity vector known, a series form solution for the velocity vector and pressure can be calculated. We admit that the convergence of these series still need to be proved before completely solving the existence of the Navier-Stokes equation and the Euler equation.

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Available abstract

In this paper, we suggest a possible series form solution to the Navier-Stokes equation and the Euler equation. With the initial velocity vector known, a series form solution for the velocity vector and pressure can be calculated. We admit that the convergence of these series still need to be proved before completely solving the existence of the Navier-Stokes equation and the Euler equation.

Key concepts: Euler equations, Compressibility, Mathematics, Euler's formula, Series (stratigraphy), Mathematical analysis, Convergence (economics), Navier–Stokes equations

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