Energy Conservative Solutions to a Nonlinear Wave System of Nematic Liquid Crystals
نویسندگان
چکیده
We establish the global existence of solutions to the Cauchy problem for a system of hyperbolic partial differential equations in one space dimension modeling a type of nematic liquid crystals that has equal splay and twist coefficients. Our results have no restrictions on the angles of the director, as we use the director in its natural three-component form, rather than the two-component form of spherical angles.
منابع مشابه
Uniqueness and Regularity of Conservative Solution to a Wave System Modeling Nematic Liquid Crystal
In this paper, a system of wave equations modeling nematic liquid crystal is considered. The solution of this system in general has gradient blowup. The global-in-time existence of Hölder continuous energy conservative solution for the initial value problem was proved in [13] by the second author, P. Zhang & Y. Zheng. In this paper, we prove the uniqueness and generic regularity of energy conse...
متن کاملNonlinear Schrodinger Equation in Nematic Liquid Crystals
We derive the amplitude equation, in the weakly nonlinear regime, for an optical wave packet that propagates in an initially undistorted nematic liquid crystal. By using the dyad representation Q i j , we find the retarded and nonlocal equation for the nematic configuration and solve it in Fourier space. This allows us to calculate the amplitude dependent dispersion relation for a nematic liqui...
متن کاملNonlinear optical transmission of lead phthalocyanine-doped nematic liquid crystal composites for multiscale nonlinear switching from nanosecond to continuous wave.
We have formulated composites of lead (II) tetrakis (4-cumylphenoxy) phthalocyanine (PbTCPc) doped into nematic liquid crystal (LC), 4(')-pentyl-4-biphenylcarbonitrile (5-CB), that has received a 90 degree twisted alignment and investigated the nonlinear transmission properties using both pulsed (Nd:YLF 524 nm, 5 ns) and cw (532 nm) lasers. In the nanosecond regime, this compound is a reverse s...
متن کاملInvestigation into the temperature dependence of isotropic- nematic phase transition of Gay- Berne liquid crystals
Density functional approach was used to study the isotropic- nematic (I-N) transition and calculate the values of freezing parameters of the Gay- Berne liquid crystal model. New direct and pair correlation functions of a molecular fluid with Gay- Berne pair potential were used. These new functions were used in density functional theory as input to calculate the isotropic- nematic transition den...
متن کاملOn Asymptotic Variational Wave Equations
We investigate the equation (ut + (f(u))x)x = f (u)(ux)/2 where f(u) is a given smooth function. Typically f(u) = u/2 or u/3. This equation models unidirectional and weakly nonlinear waves for the variational wave equation utt − c(u)(c(u)ux)x = 0 which models some liquid crystals with a natural sinusoidal c. The equation itself is also the Euler-Lagrange equation of a variational problem. Two n...
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:
دوره شماره
صفحات -
تاریخ انتشار 2012