Global solution to liquid crystal flows in three dimensions
Wenke Tan, Zhaoyang Yin
TL;DR
This paper establishes local well-posedness and global strong solutions for a 3D nematic liquid crystal flow model under small initial conditions, advancing mathematical understanding of such complex fluid systems.
Contribution
It provides the first proof of global strong solutions for the 3D liquid crystal flow system with small initial data.
Findings
Local well-posedness of the system
Existence of global strong solutions with small initial data
Mathematical framework for liquid crystal flow in three dimensions
Abstract
In this paper, we mainly study a hydrodynamic system modeling the flow of nematic liquid crystals. In three dimensions, we first establish local well-posedness of the initial-boundary value problem of the system. Then, we prove the existence of global strong solution to the system with small initial-boundary condition.
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Taxonomy
TopicsNavier-Stokes equation solutions · Geometric Analysis and Curvature Flows · Advanced Differential Equations and Dynamical Systems