A Monotonicity formula for almost self-similar suitable weak solutions to the stationary Navier-Stokes equations in $\mathbb R^5$
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866914135741038592 |
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| author | Huang, Yucong Karakhanyan, Aram |
| author_facet | Huang, Yucong Karakhanyan, Aram |
| contents | In this paper we show that a suitable weak solution to the stationary Navier-Stokes system in $\mathbb R^5$, cannot behave like a self-similar function of degree negative one if the lower limit of the local Reynolds number is finite.
To prove the result we develop a method that uses a monotonicity formula approach, classification of homogenous solutions to the incompressible Euler equations in $\mathbb R^5$, and a projection theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_02579 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Monotonicity formula for almost self-similar suitable weak solutions to the stationary Navier-Stokes equations in $\mathbb R^5$ Huang, Yucong Karakhanyan, Aram Analysis of PDEs In this paper we show that a suitable weak solution to the stationary Navier-Stokes system in $\mathbb R^5$, cannot behave like a self-similar function of degree negative one if the lower limit of the local Reynolds number is finite. To prove the result we develop a method that uses a monotonicity formula approach, classification of homogenous solutions to the incompressible Euler equations in $\mathbb R^5$, and a projection theorem. |
| title | A Monotonicity formula for almost self-similar suitable weak solutions to the stationary Navier-Stokes equations in $\mathbb R^5$ |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2511.02579 |