On basic velocity estimates for the plane steady-state Navier-Stokes system and its applications
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913366701768704 |
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| author | Korobkov, Mikhail Ren, Xiao |
| author_facet | Korobkov, Mikhail Ren, Xiao |
| contents | We consider some new estimates for general steady Navier-Stokes solutions in plane domains. According to our main result, if the domain is convex, then the difference between mean values of the velocity over two concentric circles is bounded (up to a constant factor) by the square-root of the Dirichlet integral in the annulus between the circles. The constant factor in this inequality is universal and does not depend on the ratio of the circle radii. Several applications of these formulas are discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_17884 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On basic velocity estimates for the plane steady-state Navier-Stokes system and its applications Korobkov, Mikhail Ren, Xiao Analysis of PDEs 76D05, 35Q30 We consider some new estimates for general steady Navier-Stokes solutions in plane domains. According to our main result, if the domain is convex, then the difference between mean values of the velocity over two concentric circles is bounded (up to a constant factor) by the square-root of the Dirichlet integral in the annulus between the circles. The constant factor in this inequality is universal and does not depend on the ratio of the circle radii. Several applications of these formulas are discussed. |
| title | On basic velocity estimates for the plane steady-state Navier-Stokes system and its applications |
| topic | Analysis of PDEs 76D05, 35Q30 |
| url | https://arxiv.org/abs/2405.17884 |