The hydrostatic limit of the Beris-Edwards system in dimension two

TL;DR

This paper investigates the behavior of nematic liquid crystals modeled by the Beris-Edwards system in two dimensions, establishing global well-posedness for small analytic data and analyzing the hydrostatic limit to Navier-Stokes.

Contribution

It proves the global existence of solutions for the scaled anisotropic Beris-Edwards system and rigorously justifies the hydrostatic limit in a two-dimensional setting.

Findings

Global well-posedness for small analytic data

Convergence to hydrostatic Navier-Stokes system

Validation of the hydrostatic limit in 2D

Abstract

We study the scaled anisotropic co-rotational Beris-Edwards system modeling the hydrodynamic motion of nematic liquid crystals in dimension two. We prove the global well-posedness with small analytic data in a thin strip domain. Moreover, we justify the limit to a system involving the hydrostatic Navier-Stokes system with analytic data and prove the convergence.