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arXiv · 2411.06494

On hydrostatic limit of Beris-Edwards system in a thin strip

Francesco De Anna·Xingyu Li·Marius Paicu·Arghir Zarnescu
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Abstract

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.

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Francesco De Anna, Xingyu Li, Marius Paicu, Arghir Zarnescu. 2024-11-10. On hydrostatic limit of Beris-Edwards system in a thin strip. https://arxiv.org/abs/2411.06494

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