Peer-reviewedCC BYElectronic Journal of Differential Equations
Error estimates for semi-Galerkin approximations of the 3D inhomogeneous nematic liquid crystal flows
- 1Univ. de Tarapaca, Arica, Chile
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(λk+1−1). Through higher-order H3 estimates, we then prove an convergence rate of O(λk+1−3/2) in the L2 norm. Our results provide a structure-preserving framework for the rigorous analysis of complex non-homogeneous liquid crystal flows.
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BibTeX
@article{mascarenhassilva2026error,
title = {{Error estimates for semi-Galerkin approximations of the 3D inhomogeneous nematic liquid crystal flows}},
author = {Lucas Mascarenhas-Silva and Marko Antonio Rojas-Medar},
journal = {Electronic Journal of Differential Equations},
year = {2026},
month = aug,
url = {http://ejde.math.txstate.edu/Volumes/2026/64/abstr.html},
note = {CC BY},
}
RIS
TY - JOUR
TI - Error estimates for semi-Galerkin approximations of the 3D inhomogeneous nematic liquid crystal flows
AU - Lucas Mascarenhas-Silva
AU - Marko Antonio Rojas-Medar
PY - 2026
DA - 2026/08/01
JO - Electronic Journal of Differential Equations
UR - http://ejde.math.txstate.edu/Volumes/2026/64/abstr.html
AB - 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(λ_k+1^−1). Through higher-order H^3 estimates, we then prove an convergence rate of O(λ_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.
SN - 1072-6691
ER -