Finite time blow-up for the nematic liquid crystal flow in dimension two

Abstract

We consider the initial-boundary value problem of a simplified nematic liquid crystal flow in a bounded, smooth domain $\Omega \subset {\mathbb{R}}^2$. Given any $k$ distinct points in the domain, we develop a new {\em inner--outer gluing method} to construct solutions which blow up exactly at those $k$ points as $t$ goes to a finite time $T$. Moreover, we obtain a precise description of the blow-up.

arXiv comment48pages; any comment is welcome

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Cited by in corpus (4)

• On static and hydrodynamic biaxial nematic liquid crystals
• Weak compactness of simplified nematic liquid flows in 2D
• From the Landau-de Gennes theory to the Ericksen-Leslie theory in dimension two
• New type II Finite time blow-up for the energy supercritical heat equation