Communications in Mathematical Sciences

Volume 22 (2024)

Number 6

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

Pages: 1701 – 1732

DOI: https://dx.doi.org/10.4310/CMS.2024.v22.n6.a11

Authors

Xingyu Li (BCAM, Basque Center for Applied Mathematics, Bilbao, Bizkaia, Spain; and Institut de Mathématiques de Toulouse, Université Paul Sabatier, Toulouse, France)

Marius Paicu (Université Bordeaux, Institut de Mathématiques de Bordeaux, Talence, France)

Arghir Zarnescu (Basque Center for Applied Mathematics (BCAM), Bilbao, Bizkaia, Spain; Ikerbasque, the Basque Foundation for Science, Bilbao, Spain; and the Simion Stoilow Institute of Mathematics of the Romanian Academy, Bucharest, Romania)

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.

Keywords

Beris-Edwards system, liquid crystals, Q-tensor, hydrostatic limit

2010 Mathematics Subject Classification

35Q30, 76D03

Full Text (PDF format)

Received 4 May 2023

Received revised 22 January 2024

Accepted 30 January 2024

Published 18 July 2024