Weak solutions of non-isothermal nematic liquid crystal flow in dimension three
نویسندگان
چکیده
منابع مشابه
Strong solutions of the compressible nematic liquid crystal flow
We study strong solutions of the simplified Ericksen-Leslie system modeling compressible nematic liquid crystal flows in a domain Ω ⊂ R. We first prove the local existence of unique strong solutions provided that the initial data ρ0, u0, d0 are sufficiently regular and satisfy a natural compatibility condition. The initial density function ρ0 may vanish on an open subset (i.e., an initial vacuu...
متن کاملWell-posedness of Nematic Liquid Crystal Flow
In this paper, we establish the local well-posedness for the Cauchy problem of the simplified version of hydrodynamic flow of nematic liquid crystals (1.1) in R3 for any initial data (u0, d0) having small L3 uloc -norm of (u0,∇d0). Here L3uloc(R 3) is the space of uniformly locally L3-integrable functions. For any initial data (u0, d0) with small ‖(u0,∇d0)‖L3(R3), we show that there exists a un...
متن کاملGlobal Weak Solutions to the Equations of Compressible Flow of Nematic Liquid Crystals in Two Dimensions
We consider weak solutions to a simplified Ericksen-Leslie system of two-dimensional compressible flow of nematic liquid crystals. An initialboundary value problem is first studied in a bounded domain. By developing new techniques and estimates to overcome the difficulties induced by the supercritical nonlinearity |∇d|d in the equations of angular momentum on the direction field, and adapting t...
متن کاملWeak anchoring energy and pretilt of a nematic liquid crystal
2014 We extend the wedge technique of Rivière et al. to measure the pretilt angle 03A6 and the (weak) anchoring energy of a nematic liquid crystal oriented on a suitably treated glass surface. The liquid crystal is placed in a wedge shaped space formed by the plate to be studied and a « standard » plate giving a strong homeotropic anchoring. Instead of using a total reflection technique, we mea...
متن کاملBlow up criterion for compressible nematic liquid crystal flows in dimension three
In this paper, we consider the short time strong solution to a simplified hydrodynamic flow modeling the compressible, nematic liquid crystal materials in dimension three. We establish a criterion for possible breakdown of such solutions at finite time in terms of the temporal integral of both the maximum norm of the deformation tensor of velocity gradient and the square of maximum norm of grad...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Elliptic and Parabolic Equations
سال: 2020
ISSN: 2296-9020,2296-9039
DOI: 10.1007/s41808-020-00055-z