Continuation criterion for the 2D liquid crystal flows (Q429069)

Summary: 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 \(\nabla d, \partial_t d \in L^1(0, T; \dot{B}^0_{\infty,\infty}(\mathbb R^2))\) 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.