Regularity of Solutions to 3-d Nematic Liquid Crystal Flows

نویسندگان

  • QIAO LIU
  • SHANGBIN CUI
چکیده

In this note we consider the regularity of solutions to 3-D nematic liquid crystal flows, we prove that if either u ∈ Lq(0, T ;Lp(R3)), 2 q + 3 p ≤ 1, 3 < p ≤ ∞; or u ∈ Lα(0, T ;Lβ(R3)), 2 α + 3 β ≤ 2, 3 2 < β ≤ ∞, then the solution (u, d) is regular on (0, T ].

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Director Structures in a Chiral Nematic Slab: Threshold Field and Pitch Variations

Abstract The liquid crystal director distribution is determined for a confined chiral nematic slab. The molecular director distribution of the field-controlled chiral nematic slab is directly calculated. The director profiles for the tilt and the twist angles, under different applied fields, are calculated in the slab with weak boundary conditions. Then, the dependence of the threshold field on...

متن کامل

Liquid crystal flows in two dimensions

The paper is concerned with a simplified hydrodynamic equation, proposed by Ericksen and Leslie, modeling the flow of nematic liquid crystals. In dimension two, we establish both interior and boundary regularity theorem for such a flow under smallness conditions. As a consequence, we establish the existence of global weak solutions that are smooth away from at most finitely many singular times ...

متن کامل

Global Solution to the Nematic Liquid Crystal Flows with Heat Effect

This paper is devoted to studying the temperature-dependent incompressible nematic liquid crystal flows in a bounded domain Ω ⊂ R (N = 2, 3). Inspired by Danchin [J. Math. Fluid Mech. 2006], we use a localization argument to recover the maximal regularity of Stokes equation with variable viscosity. Also the results proved by Lei-Li-Zhang [Proc. Amer. Math. Soc. 2014] are generalized to the case...

متن کامل

Numerical Investigation of Director Orientation and Flow of Nematic Liquid Crystal in a Planar 1:4 Expansion

In this paper, numerical solutions to the equations for the Ericksen-Leslie dynamic theory are obtained for two-dimensional nematic liquid crystal flows subject to a magnetic field. A numerical method for solving the governing equations for 2D flows has been formulated. The governing equations are solved by a finite difference technique based on the GENSMAC methodology introduced by Tomé and Mc...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2010