282 research outputs found
Global Strong Solutions of the Full Navier-Stokes and Q-Tensor System for Nematic Liquid Crystal Flows in Two Dimensions
We consider a full Navier-Stokes and Q-tensor system for incompressible liquid crystal flows of nematic type. In the two dimensional periodic case, we prove the existence and uniqueness of global strong solutions that are uniformly bounded in time. This result is obtained without any smallness assumption on the physical parameter ξ that measures the ratio between tumbling and aligning effects of a shear flow exerting over the liquid crystal directors. Moreover, we show the uniqueness of asymptotic limit for each global strong solution as time goes to infinity and provide an uniform estimate on the convergence rate. © 2016 Society for Industrial and Applied Mathematics
Global strong solutions of the full Navier-Stokes and -tensor system for nematic liquid crystal flows in : existence and long-time behavior
We consider a full Navier-Stokes and -tensor system for incompressible
liquid crystal flows of nematic type. In the two dimensional periodic case, we
prove the existence and uniqueness of global strong solutions that are
uniformly bounded in time. This result is obtained without any smallness
assumption on the physical parameter that measures the ratio between
tumbling and aligning effects of a shear flow exerting over the liquid crystal
directors. Moreover, we show the uniqueness of asymptotic limit for each global
strong solution as time goes to infinity and provide an uniform estimate on the
convergence rate
Global strong solutions of the full Navier-Stokes and Q-tensor system for nematic liquid crystal flows in two dimensions
We consider a full Navier-Stokes and Q-tensor system for incompressible liquid crystal flows of nematic type. In the two dimensional periodic case, we prove the existence and uniqueness of global strong solutions that are uniformly bounded in time. This result is obtained without any smallness assumption on the physical parameter. that measures the ratio between tumbling and aligning effects of a shear flow exerting over the liquid crystal directors. Moreover, we show the uniqueness of asymptotic limit for each global strong solution as time goes to infinity and provide an uniform estimate on the convergence rate
Global well-posedness for the dynamical Q-tensor model of liquid crystals
In this paper, we consider a complex fluid modeling nematic liquid crystal
flows, which is described by a system coupling Navier-Stokes equations with a
parabolic Q-tensor system. We first prove the global existence of weak
solutions in dimension three. Furthermore, the global well-posedness of strong
solutions is studied with sufficiently large viscosity of fluid. Finally, we
show a continuous dependence result on the initial data which directly yields
the weak-strong uniqueness of solutions
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