Weak global attractor for the $3D$-Navier-Stokes equations via the globally modified Navier-Stokes equations
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2024
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| author | Bortolan, Matheus Cheque de Carvalho, Alexandre Nolasco Marín-Rubio, Pedro Valero, José |
| author_facet | Bortolan, Matheus Cheque de Carvalho, Alexandre Nolasco Marín-Rubio, Pedro Valero, José |
| contents | In this paper we obtain the existence of a weak global attractor for the three-dimensional Navier-Stokes equations, that is, a weakly compact set with an invariance property, that uniformly attracts solutions, with respect to the weak topology, for initial data in bounded sets. To that end, we define this weak global attractor in terms of limits of solutions of the globally modified Navier-Stokes equations in the weak topology. We use the theory of semilinear parabolic equations and $ε$-regularity to obtain the local well posedness for the globally modified Navier-Stokes equations and the existence of a global attractor and its regularity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_06435 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Weak global attractor for the $3D$-Navier-Stokes equations via the globally modified Navier-Stokes equations Bortolan, Matheus Cheque de Carvalho, Alexandre Nolasco Marín-Rubio, Pedro Valero, José Analysis of PDEs Dynamical Systems 35Q30, 35B41, 35K58, 76D05 In this paper we obtain the existence of a weak global attractor for the three-dimensional Navier-Stokes equations, that is, a weakly compact set with an invariance property, that uniformly attracts solutions, with respect to the weak topology, for initial data in bounded sets. To that end, we define this weak global attractor in terms of limits of solutions of the globally modified Navier-Stokes equations in the weak topology. We use the theory of semilinear parabolic equations and $ε$-regularity to obtain the local well posedness for the globally modified Navier-Stokes equations and the existence of a global attractor and its regularity. |
| title | Weak global attractor for the $3D$-Navier-Stokes equations via the globally modified Navier-Stokes equations |
| topic | Analysis of PDEs Dynamical Systems 35Q30, 35B41, 35K58, 76D05 |
| url | https://arxiv.org/abs/2402.06435 |