Nematic Liquid Crystals in Lipschitz domains

Abstract

We consider the simplified Ericksen-Leslie model in three dimensional bounded Lipschitz domains. Applying a semilinear approach, we prove local and global well-posedness (assuming a smallness condition on the initial data) in critical spaces for initial data in $L_{\sigma }^3$ for the fluid and $W^{1,3}$ for the director field. The analysis of such models, so far, has been restricted to domains with smooth boundaries.

References in corpus (2)

• Well-Posedness of Nematic Liquid Crystal Flow in $L_{uloc}^3({\mathbb{R}}^3)$
• Resolvent Estimates in L^p for the Stokes Operator in Lipschitz Domains

Cited by in corpus (2)

• Maximal $L^p$-regularity and $H^{\infty }$-calculus for block operator matrices and applications
• The Stokes operator in two-dimensional bounded Lipschitz domains