107 citations · 244 across the 21 of their papers we have counts for
4 papers · 1 filter
Regularity of a gradient flow generated by the anisotropic Landau-de Gennes energy with a singular potential
Yuning Liu, Xinyang Lu, Xiang Xu
In this paper we study a gradient flow generated by the Landau-de Gennes free energy that describes nematic liquid crystal configurations in the space of -tensors. This free ene…
Blowup rate estimates of the Ball-Majumdar potential and its gradient in the Landau-de Gennes theory
Xinyang Lu, Xiang Xu, Wujun Zhang
In this paper we revisit a singular bulk potential in the Landau-de Gennes free energy that describes nematic liquid crystal configurations in the framework of the Q-tensor order p…
Analysis for Allen-Cahn-Ohta-Nakazawa Model in a Ternary System
Sookyung Joo, Xiang Xu, Yanxiang Zhao
In this paper we study the global well-posedness of the Allen-Cahn Ohta-Nakazawa model with two fixed nonlinear volume constraints. Utilizing the gradient flow structure of its fre…
Maximum Principle Preserving Schemes for Binary Systems with Long-range Interactions
Xiang Xu, Yanxiang Zhao
We study some maximum principle preserving and energy stable schemes for the Allen-Cahn-Ohta-Kawasaki model with fixed volume constraint. With the inclusion of a nonlinear term in…