Attractors and their dimensions for the 3D Fractional Navier--Stokes--Voigt Equations
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908635275198464 |
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| author | Ilyin, Alexei Kalantarov, Varga Zelik, Sergey |
| author_facet | Ilyin, Alexei Kalantarov, Varga Zelik, Sergey |
| contents | We study the dimensions of the attractors for the fractional Navier--Stokes--Voigt equations. These equations, which include a fractional order of the Stokes operator applied to the time derivative, serve as natural extensions and regularizations of the classical Navier--Stokes equations. We give a comprehensive analysis of the upper bounds for the fractal dimensions of the attractor in terms of the relevant physical parameters based on the advanced spectral inequalities such as Lieb--Thirring and Cwikel--Lieb--Rosenblum inequalities. These results extend previous works on the classical Navier--Stokes--Voigt system to the fractional setting and give an essential improvement of the estimates known before for the non-fractional case as well. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_04783 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Attractors and their dimensions for the 3D Fractional Navier--Stokes--Voigt Equations Ilyin, Alexei Kalantarov, Varga Zelik, Sergey Analysis of PDEs 35Q30, 35B41, 37L30 We study the dimensions of the attractors for the fractional Navier--Stokes--Voigt equations. These equations, which include a fractional order of the Stokes operator applied to the time derivative, serve as natural extensions and regularizations of the classical Navier--Stokes equations. We give a comprehensive analysis of the upper bounds for the fractal dimensions of the attractor in terms of the relevant physical parameters based on the advanced spectral inequalities such as Lieb--Thirring and Cwikel--Lieb--Rosenblum inequalities. These results extend previous works on the classical Navier--Stokes--Voigt system to the fractional setting and give an essential improvement of the estimates known before for the non-fractional case as well. |
| title | Attractors and their dimensions for the 3D Fractional Navier--Stokes--Voigt Equations |
| topic | Analysis of PDEs 35Q30, 35B41, 37L30 |
| url | https://arxiv.org/abs/2511.04783 |