Nematic Liquid Crystal Flow with Partially Free Boundary

Fanghua Lin, Yannick Sire, Juncheng Wei, Yifu Zhou

Research output: Contribution to journalArticlepeer-review


We study a simplified Ericksen–Leslie system modeling the flow of nematic liquid crystals with partially free boundary conditions. It is a coupled system between the Navier–Stokes equation for the fluid velocity with a transported heat flow of harmonic maps, and both of these parabolic equations are critical for analysis in two dimensions. The boundary conditions are physically natural and they correspond to the Navier slip boundary condition with zero friction for the velocity field and a Plateau–Neumann type boundary condition for the map. In this paper we construct smooth solutions of this coupled system that blow up in finite time at any finitely many given points on the boundary or in the interior of the domain.

Original languageEnglish (US)
Article number20
JournalArchive for Rational Mechanics and Analysis
Issue number2
StatePublished - Apr 2023

ASJC Scopus subject areas

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering


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