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2021•arXiv (Cornell University)Open access

There exist blow-ups in the incompressible Navier-Stokes equation

Yanyou Qiao

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Abstract

In this paper, we solve the Navier-Stokes equation, one of the seven Millennium Prize Problems suggested by Clay Mathematics Institute(CMI). We prove that, for any initial velocity u0, there has been a force vector f, such that there exists no smooth solution to the respective Navier-Stokes equation. This result also holds for the Euler equation.

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What this paper is about

In this paper, we solve the Navier-Stokes equation, one of the seven Millennium Prize Problems suggested by Clay Mathematics Institute(CMI). We prove that, for any initial velocity u0, there has been a force vector f, such that there exists no smooth solution to the respective Navier-Stokes equation. This result also holds for the Euler equation.

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Available abstract

In this paper, we solve the Navier-Stokes equation, one of the seven Millennium Prize Problems suggested by Clay Mathematics Institute(CMI). We prove that, for any initial velocity u0, there has been a force vector f, such that there exists no smooth solution to the respective Navier-Stokes equation. This result also holds for the Euler equation.

Key concepts: Compressibility, Euler equations, Navier–Stokes equations, Mathematics, Mathematical analysis, Euler's formula, Hagen–Poiseuille flow from the Navier–Stokes equations, Velocity vector

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