Global Existence and Regularity for the Full Coupled Navier-Stokes and Q-Tensor System
نویسندگان
چکیده
In this paper we study the full system of incompressible liquid crystals, as modelled in the Qtensor framework. Under certain conditions we prove the global existence of weak solutions in dimension two or three and the existence of global regular solutions in dimension two. We also prove the weak-strong uniqueness of the solutions, for suficiently regular initial data.
منابع مشابه
Energy Dissipation and Regularity for a Coupled Navier-Stokes and Q-Tensor System
We study a complex non-newtonian fluid that models the flow of nematic liquid crystals. The fluid is described by a system that couples a forced Navier-Stokes system with a parabolic-type system. We prove the existence of global weak solutions in dimensions two and three. We show the existence of a Lyapunov functional for the smooth solutions of the coupled system and use the cancellations that...
متن کاملWeak Time Regularity and Uniqueness for a Q-Tensor Model
The coupled Navier-Stokes and Q-Tensor system is one of the models used to describe the behavior of the nematic liquid crystals. The existence of weak solutions and a uniqueness criteria have been already studied (see [11] for a Cauchy problem in the whole R3 and [7] for a initial-boundary problem in a bounded domain Ω). Nevertheless, results on strong regularity have only been treated in [11] ...
متن کاملWell-Posedness of a Fully Coupled Navier-Stokes/Q-tensor System with Inhomogeneous Boundary Data
We prove short-time well-posedness and existence of global weak solutions of the Beris–Edwards model for nematic liquid crystals in the case of a bounded domain with inhomogeneous mixed Dirichlet and Neumann boundary conditions. The system consists of the Navier-Stokes equations coupled with an evolution equation for the Q-tensor. The solutions possess higher regularity in time of order one com...
متن کاملGlobal 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 o...
متن کاملFe b 20 07 Global well - posedness for a Smoluchowski equation coupled with Navier - Stokes equations in 2
We prove global existence for a nonlinear Smoluchowski equation (a nonlinear Fokker-Planck equation) coupled with Navier-Stokes equations in 2d. The proof uses a deteriorating regularity estimate in the spirit of [5] (see also [1])
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- SIAM J. Math. Analysis
دوره 43 شماره
صفحات -
تاریخ انتشار 2011