Lucas Mascarenhas-Silva, Marko Rojas-Medar
Abstract:
This work investigates rigorously the convergence properties of a spectral
semi-Galerkin approximation for three-dimensional inhomogeneous nematic
liquid crystal flows. To overcome the analytical barriers posed by the
hyperbolic density transport and the pointwise geometric constraint \(|d|=1\),
we analyze a decoupled scheme that projects only the velocity onto a
finite-dimensional space. Assuming uniform local-in-time bounds, we first
derive basic error estimates of order \(O(\lambda_{k+1}^{-1})\).
Through higher-order \(H^3\) estimates, we then prove an convergence rate of
\(O(\lambda_{k+1}^{-3/2})\) in the \(L^2\) norm.
Our results provide a structure-preserving framework for the rigorous analysis
of complex non-homogeneous liquid crystal flows.
Submitted April 21, 2026. Published August 28, 2026.
Math Subject Classifications: 35Q35, 76A15, 65M12, 65M15, 65M60.
Key Words: Inhomogeneous nematic liquid crystals; spectral semi-Galerkin method; error estimates; convergence rate.
DOI: 10.58997/ejde.2026.64
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Lucas Mascarenhas-Silva Programa de Doctorado en Ciencias con Mención en Matemática Departamento de Matemática Universidad de Tarapacá Casilla 7D, Arica, Chile email: lucas.mascarenhas.silva@alumnos.uta.cl |
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Marko Rojas-Medar Departamento de Matemática Facultad de Ciencias Universidad de Tarapacá Arica, Chile email: mmedar@academicos.uta.cl |
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