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arXiv · 2506.05152

The $\mathcal{R}$-boundedness of solution operators for the $Q$-tensor model of nematic liquid crystals

Daniele Barbera·Miho Murata
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Abstract

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

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Daniele Barbera, Miho Murata. 2025-06-05. The $\mathcal{R}$-boundedness of solution operators for the $Q$-tensor model of nematic liquid crystals. https://arxiv.org/abs/2506.05152

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