Regularity of solutions of the Navier-Stokes-αβ equations with wall-eddy boundary conditions
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911340711378944 |
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| author | Rotundo, Nella Tsogtgerel, Gantumur |
| author_facet | Rotundo, Nella Tsogtgerel, Gantumur |
| contents | We establish global well-posedness and regularity for the Navier-Stokes-αβ system endowed with the wall-eddy boundary conditions proposed by Fried and Gurtin (2008). These conditions introduce a tangential vorticity traction proportional to wall vorticity and provide a continuum-mechanical model for near-wall turbulence. Our analysis begins with a variational formulation of the stationary fourth-order system, where we prove symmetry and a Gårding inequality for the associated bilinear form. We then verify Douglis-Nirenberg ellipticity and the Lopatinskii-Shapiro covering condition, establishing full Agmon-Douglis-Nirenberg regularity for the coupled system. Building on this framework, we derive a hierarchy of energy estimates for the nonlinear evolution equation, which yields global regularity, uniqueness, and stability. To our knowledge, this provides the first complete analytical treatment of the wall-eddy boundary model of Fried and Gurtin. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_22436 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Regularity of solutions of the Navier-Stokes-αβ equations with wall-eddy boundary conditions Rotundo, Nella Tsogtgerel, Gantumur Analysis of PDEs 35Q30 We establish global well-posedness and regularity for the Navier-Stokes-αβ system endowed with the wall-eddy boundary conditions proposed by Fried and Gurtin (2008). These conditions introduce a tangential vorticity traction proportional to wall vorticity and provide a continuum-mechanical model for near-wall turbulence. Our analysis begins with a variational formulation of the stationary fourth-order system, where we prove symmetry and a Gårding inequality for the associated bilinear form. We then verify Douglis-Nirenberg ellipticity and the Lopatinskii-Shapiro covering condition, establishing full Agmon-Douglis-Nirenberg regularity for the coupled system. Building on this framework, we derive a hierarchy of energy estimates for the nonlinear evolution equation, which yields global regularity, uniqueness, and stability. To our knowledge, this provides the first complete analytical treatment of the wall-eddy boundary model of Fried and Gurtin. |
| title | Regularity of solutions of the Navier-Stokes-αβ equations with wall-eddy boundary conditions |
| topic | Analysis of PDEs 35Q30 |
| url | https://arxiv.org/abs/2512.22436 |