10 citations · 29 across the 10 of their papers we have counts for
9 papers · 1 filter
On the triple junction problem with general surface tension coefficients
Nicholas D. Alikakos, Zhiyuan Geng
We investigate the Allen-Cahn system \begin{equation*} Δu-W_u(u)=0,\quad u:\mathbb{R}^2\rightarrow\mathbb{R}^2, \end{equation*} where is a pote…
On the triple junction problem on the plane without symmetry hypotheses
Nicholas D. Alikakos, Zhiyuan Geng
We investigate the Allen-Cahn system \begin{equation*} Δu-W_u(u)=0,\quad u:\mathbb{R}^2\rightarrow\mathbb{R}^2, \end{equation*} where is a pote…
Uniform profile near the point defect of Landau-de Gennes model
Zhiyuan Geng, Arghir Zarnescu
For the Landau-de Gennes functional on 3D domains, \begin{equation*} I_{\varepsilon}(Q,Ω):=\int_Ω\left\{\frac{1}{2}|\nabla Q|^2+\frac{1}{\varepsilon^2}\left( -\frac{a^2}{2}\mathrm{…
A unified approach towards the impossibility of finite time vanishing depth for incompressible free boundary flows
Zhiyuan Geng, Rafael Granero-Belinchón
In this paper we study the motion of an internal water wave and an internal wave in a porous medium. For these problems we establish that, if the free boundary and, in the case of…
Two dimensional liquid crystal droplet problem with tangential boundary condition
Zhiyuan Geng, Fanghua Lin
This paper studies a shape optimization problem which reduces to a nonlocal free boundary problem involving perimeter. It is motivated by a study of liquid crystal droplets with a…
Large asymptotics for minimal partitions of the Dirichlet eigenvalue
Zhiyuan Geng, Fanghua Lin
In this paper, we study large asymptotics of the minimal -partition problem for Dirichlet eigenvalue. For any smooth domain such that , we p…
Point defects in 2-D liquid crystals with singular potential: profiles and stability
Zhiyuan Geng, Wei Wang
We study radial symmetric point defects with degree in 2D disk or in -tensor framework with singular bulk energy, which is defined by Bingham closu…
Regularity of Minimizers of a Tensor-valued Variational Obstacle Problem in Three Dimensions
Zhiyuan Geng, Jiajun Tong
Motivated by Ball and Majumdar's modification of Landau-de Gennes model for nematic liquid crystals, we study energy-minimizer of a tensor-valued variational obstacle problem i…
Stability of half-degree point defect profiles for 2-D nematic liquid crystal
Zhiyuan Geng, Wei Wang, Pingwen Zhang +1
In this paper, we prove the stability of half-degree point defect profiles in for the nematic liquid crystal within Landau-de Gennes model.