Continuation Criterion for the 2D Liquid Crystal Flows

Abstract EN

We consider the 2D liquid crystal systems, which consists of Navier-Stokes system coupled with wave maps or biharmonic wave maps, respectively.

By logarithmic Sobolev inequalities, we obtain a blow-up criterion ∇d,∂td∈L1(0,T;B˙∞,∞0(ℝ2)) for the case with wave maps, and we prove the existence of a global-in-time strong solutions for the case with biharmonic wave maps.