On hydrostatic limit of Beris-Edwards system in a thin strip
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866912118211608576 |
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| author | De Anna, Francesco Li, Xingyu Paicu, Marius Zarnescu, Arghir |
| author_facet | De Anna, Francesco Li, Xingyu Paicu, Marius Zarnescu, Arghir |
| contents | In this paper we consider the 3D co-rotational Beris-Edwards system modeling the hydrodynamic motion of nematic liquid crystals in a thin strip. The system contains the incompressible Navier-Stokes, coupled with a parabolic system for matrix-valued functions, the $Q$-tensors.
We show that under a suitable scaling, corresponding, in the Navier-Stokes part, to the hydrostatic scaling, one obtains in the limit a partly decoupled system. For the fluid part we obtain the Prandtl system while for the $Q$-tensors we obtain a non-standard system, involving fluids components and a non-standard combination of partly dissipative equations and algebraic constraints.
We prove the convergence of the rescaled system and the well-posedness of the limit in Sobolev spaces. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_06494 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On hydrostatic limit of Beris-Edwards system in a thin strip De Anna, Francesco Li, Xingyu Paicu, Marius Zarnescu, Arghir Analysis of PDEs In this paper we consider the 3D co-rotational Beris-Edwards system modeling the hydrodynamic motion of nematic liquid crystals in a thin strip. The system contains the incompressible Navier-Stokes, coupled with a parabolic system for matrix-valued functions, the $Q$-tensors. We show that under a suitable scaling, corresponding, in the Navier-Stokes part, to the hydrostatic scaling, one obtains in the limit a partly decoupled system. For the fluid part we obtain the Prandtl system while for the $Q$-tensors we obtain a non-standard system, involving fluids components and a non-standard combination of partly dissipative equations and algebraic constraints. We prove the convergence of the rescaled system and the well-posedness of the limit in Sobolev spaces. |
| title | On hydrostatic limit of Beris-Edwards system in a thin strip |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2411.06494 |