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The $\mathcal{R}$-boundedness of solution operators for the Q-tensor model of nematic liquid crystals in $\mathbb{R}^{N}$ and $\mathbb{R}^{N}_{+}$

Daniele Barbera and Miho Murata

Vol. 8 (2026), No. 4, 779–833
Abstract

We consider a resolvent problem arising from the Q-tensor model for nematic liquid crystal flows in the half-space. Our purpose is to show the ℛ-boundedness for the solution operator families of the resolvent problem when the resolvent parameter lies near the origin. The definition of the ℛ-solvability implies the uniform boundedness of the operator and, consequently, the resolvent estimates for the linear system.

Keywords
$\mathcal{R}$-boundedness, resolvent problem, resolvent estimate, Q-tensor model, nematic liquid crystals
Mathematical Subject Classification
Primary: 35A01, 35Q30, 35Q35, 76A15
Milestones
Received: 3 September 2025
Revised: 9 April 2026
Accepted: 12 August 2026
Published: 15 October 2026
Authors
Daniele Barbera
Technical University of Sofia
Sofia
Bulgaria
Miho Murata
Shizuoka University
Shizuoka
Japan