Work

Nematic liquid crystals: Ericksen-Leslie theory with general stress tensors

Year: 2025

Type: article

Abstract: The Ericksen-Leslie model for nematic liquid crystal flows in case of an isothermal and incompressible fluid with general Leslie stress and anisotropic elasticity, i.e. with general Ericksen stress tensor, is shown for the first time to be strongly well-posed. Of central importance is a fully nonlinear boundary condition for the director field, which, in this generality, is necessary to guarantee that the system fulfills physical principles. The system is shown to be locally, strongly well-posed in the $$L_p$$ L p -setting. More precisely, the existence and uniqueness of a local, strong $$L_p$$ L p -solution to the general system is proved and it is shown that the director d satisfies $$|d|_2\equiv 1$$ | d | 2 ≡ 1 provided this holds for its initial data $$d_0$$ d 0 . In addition, the solution is shown to depend continuously on the data. The results are proven without any structural assumptions on the Leslie coefficients and in particular without assuming Parodi’s relation.

Source: Archive for Rational Mechanics and Analysis

DOI: 10.1007/s00205-025-02150-8

Authors: Matthias Hieber, Jinkai Li, Mathias Wilke

Institutions: Technische Universität Darmstadt, South China Normal University, Martin Luther University Halle-Wittenberg

Language: English

Topic: Navier-Stokes equation solutions

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funders: Deutsche Forschungsgemeinschaft, National Natural Science Foundation of China, Martin-Luther-Universität Halle-Wittenberg