Blow-up suppression for the nematic liquid crystal flow via Couette flow on $\mathbb{R}^2$
Analysis of PDEs
2026-02-03 v1
Abstract
As is well known, for the harmonic heat flow or liquid crystal flow in two-dimension, the solution may blow up when the initial energy is greater than . Motivated by Lai--Lin--Wang--Wei--Zhou (CPAM, 2022), where singular solutions were constructed in the presence of small-scale velocity fields, it is natural to ask whether large-scale velocities may play a stabilizing role, preventing the concentration of blow-up. Here we show that the blow-up phenomenon can be suppressed by a Couette flow whose amplitude is large enough under a weak assumption on the anisotropic norm of the initial data. In particular, we construct examples with initial energy exceeding that satisfy our assumptions.
Cite
@article{arxiv.2602.01823,
title = {Blow-up suppression for the nematic liquid crystal flow via Couette flow on $\mathbb{R}^2$},
author = {Yubo Chen and Wendong Wang and Juncheng Wei and Guoxu Yang},
journal= {arXiv preprint arXiv:2602.01823},
year = {2026}
}