Symplectic Representation and Turbulent Global Solutions of Incompressible Navier-Stokes Equations in $\R^3$

Yongqian Han

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arXiv · 2311.18308

Symplectic Representation and Turbulent Global Solutions of Incompressible Navier-Stokes Equations in $\R^3$

Yongqian Han

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Abstract

The incompressible Navier-Stokes equations are considered. We find that there exist infinite non-trivial solutions of static Euler equations. Moreover there exist random solutions of static Euler equations. Provided Reynolds number is large enough and time variable $t$ goes to infinity, these random solutions of static Euler equations are the path limits of corresponding Navier-Stokes flows. But the double limit of these Navier-Stokes flows do not exist. Therefore these solutions are called turbulent solutions.

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Yongqian Han. 2023-11-30. Symplectic Representation and Turbulent Global Solutions of Incompressible Navier-Stokes Equations in $\R^3$. https://arxiv.org/abs/2311.18308

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