Symplectic Representation and Turbulent Global Solutions of Incompressible Navier-Stokes Equations in $\R^3$
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916332268683264 |
|---|---|
| author | Han, Yongqian |
| author_facet | Han, Yongqian |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_18308 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Symplectic Representation and Turbulent Global Solutions of Incompressible Navier-Stokes Equations in $\R^3$ Han, Yongqian Analysis of PDEs Mathematical Physics 35Q30, 76D05, 76F02, 37L20 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. |
| title | Symplectic Representation and Turbulent Global Solutions of Incompressible Navier-Stokes Equations in $\R^3$ |
| topic | Analysis of PDEs Mathematical Physics 35Q30, 76D05, 76F02, 37L20 |
| url | https://arxiv.org/abs/2311.18308 |