Through a unit cotangent vector field A ∈ TM, we define the Oseen–Frank energy functional on 3-dimensional Riemannian manifolds. Moreover, we prove partial regularity of minimizers of the Oseen–Frank energy on 3-dimensional Riemannian manifolds....
Zarnescu, "Landau-de gennes theory of nematic liquid crystals: the oseen-frank limit and beyond," Arch. Rat. Mech. Anal. 196(1), pp. 227-280, 2010.A. Majumdar and A. Zarnescu. Landau-de gennes theory of nematic liquid crystals: the oseen-frank limit and beyond. Archive for Rational...
arXiv:1703.02214v1 [math.AP] 7 Mar 2017WELL-POSEDNESS OF THE ERICKSEN-LESLIE SYSTEM FORTHE OSEEN-FRANK MODEL IN L 3uloc (R3 )MIN-CHUN HONG AND YU MEIAbstract. We investigate the Ericksen-Leslie system for the Oseen-Frankmodel with unequal Frank elastic constants in R 3 . To generalize ...
Well-posedness of the Ericksen-Leslie System for the Oseen-Frank Model in L^3_{uloc}(\\mathbb{R}^3) We investigate the Ericksen-Leslie system for the Oseen-Frank model with unequal Frank elastic constants in $\\mathbb{R}^3$. To generalize the result of Hi... MC Hong,M Yu 被引量...
These 12 arguments are independent variables in the Frank-Oseen energy density FF. The independence of n⃗ n→ and TT in F(n⃗ ,T)F(n→,T) is similar to the independence of qq and vv in the Lagrangian L(q,v,t)L(q,v,t) for point mechanics. It may seem a bit pedantic to...
In the first part of this paper, we establish global existence of solutions\nof the liquid crystal (gradient) flow for the well-known Oseen-Frank model. The\nliquid crystal flow is a prototype of equations from the Ericksen-Leslie system\nin the hydrodynamic theory and generalizes the heat ...
Moreover, the convergence is\nuniform in the interior of the domain, away from the singularities of the\nlimiting Oseen-Frank global minimizer. We obtain results on the rate of\nconvergence of the eigenvalues and the regularity of the eigenvectors of the\nLandau-De Gennes global minimizer.\nW...
Measure-valued solutions to the Ericksen-Leslie model equipped with the Oseen-Frank energy. To appear in: Nonli. Anal., 2018.R. Lasarzik. Weak-strong uniqueness for measure-valued solutions to the Ericksen-Leslie model equipped with the Oseen- Frank free energy. ArXiv e-prints, 1711.03371, ...
P. Xin, Global existence of solutions of the liquid crystal flow for the Oseen-Frank model in R2, Adv. Math., 231 (2012), 1364-1400.M. C. Hong, Z. P. Xin, Global existence of solutions of the Liquid Crystal flow for the Oseen-Frank model in R2. Adv. Math., 231 (2012), ...
defectsRenormalized EnergyIn this paper we discuss the behavior of the Oseen-Frank modelfor nematic liquid crystals in the limit of vanishing thickness. More precisely,in a thin slab Ω× (0, h) with Ω ? ~R2 and h > 0 we consider the one-constantapproximation of the Oseen-Frank model ...