107 citations · 244 across the 21 of their papers we have counts for
21 papers
Exponential decay for the 3D Boussinesq equations with Navier boundary conditions
Wen Feng, Weinan Wang, Xiang Xu
We study the three-dimensional incompressible Boussinesq equations on a bounded domain with smooth boundary and Navier boundary conditions. We construct global weak solutions by a…
Contact set of solutions to gradient flow of Landau-de Gennes energy with a singular entropy potential
Yuning Liu, Xiang Xu
This paper investigates the convexity structure and contact set of the -tensor flow with anisotropic Landau--de Gennes elastic energy and a singular entropy potential . Th…
Inverse boundary value problems of determining nonlinear coefficients for the JMGT equation
Dong Qiu, Xiang Xu, Yeqiong Ye +1
We consider inverse boundary value problems for the Jordan-Moore-Gibson-Thompson (JMGT) equation in nonlinear acoustics with quadratic nonlinearities of Kuznetsov-type and Westerve…
Singularity formation for full Ericksen-Leslie system of nematic liquid crystal flows in dimension two
Geng Chen, Tao Huang, Xiang Xu
In this paper, we prove the singularity formation for Poiseuille laminar flow of full Ericksen-Leslie system modeling nematic liquid crystal flows in dimension two. The singularity…
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…
Energy stable semi-implicit schemes for Allen-Cahn-Ohta-Kawasaki Model in Binary System
Xiang Xu, Yanxiang Zhao
In this paper, we propose a first order energy stable linear semi-implicit method for solving the Allen-Cahn-Ohta-Kawasaki equation. By introducing a new nonlinear term in the Ohta…
Global Well-posedness of the Two Dimensional Beris-Edwards System with General Laudau-de Gennes Free Energy
Yuning Liu, Hao Wu, Xiang Xu
In this paper, we consider the Beris-Edwards system for incompressible nematic liquid crystal flows. The system under investigation consists of the Navier-Stokes equations for the…
An elementary proof of eigenvalue preservation for the co-rotational Beris-Edwards system
Andres Contreras, Xiang Xu, Wujun Zhang
We study the co-rotational Beris-Edwards system modeling nematic liquid crystals and revisit the eigenvalue preservation property discussed in \cite{XZ16}. We give an alternative b…
Dynamics and flow effects in the Beris-Edwards system modelling nematic liquid crystals
Hao Wu, Xiang Xu, Arghir Zarnescu
We consider the Beris-Edwards system modelling incompressible liquid crystal flows of nematic type. This couples a Navier-Stokes system for the fluid velocity with a parabolic reac…
Global strong solutions of the full Navier-Stokes and -tensor system for nematic liquid crystal flows in : existence and long-time behavior
Cecilia Cavaterra, Elisabetta Rocca, Hao Wu +1
We consider a full Navier-Stokes and -tensor system for incompressible liquid crystal flows of nematic type. In the two dimensional periodic case, we prove the existence and uni…
A Wasserstein gradient flow approach to Poisson-Nernst-Planck equations
David Kinderlehrer, Léonard Monsaingeon, Xiang Xu
The Poisson-Nernst-Planck system of equations used to model ionic transport is interpreted as a gradient flow for the Wasserstein distance and a free energy in the space of probabi…
Dynamic Cubic Instability in a 2D Q-tensor Model for Liquid Crystals
Gautam Iyer, Xiang Xu, Arghir Zarnescu
We consider a four-elastic-constant Landau-de Gennes energy characterizing nematic liquid crystal configurations described using the -tensor formalism. The energy contains a cub…
On the rigidity of nematic liquid crystal flow on
Changyou Wang, Xiang Xu
In this paper we establish the uniformity property of a simplified Ericksen-Leslie system modelling the hydrodynamics of nematic liquid crystals on the two dimensional unit sphere…
Global weak solution for a coupled compressible Navier-Stokes and Q-tensor system
Dehua Wang, Xiang Xu, Cheng Yu
In this paper, we study a coupled compressible Navier-Stokes/Q-tensor system modeling the nematic liquid crystal flow in a three-dimensional bounded spatial domain. The existence a…
Analysis of a diffuse-interface model for the binary viscous incompressible fluids with thermo-induced Marangoni effects
Hao Wu, Xiang Xu
In this paper we study the well-posedness and long-time dynamics of a diffuse-interface model for the mixture of two viscous incompressible Newtonian fluids with thermo-induced Mar…
Strong solutions, global regularity and stability of a hydrodynamic system modeling vesicle and fluid interactions
Hao Wu, Xiang Xu
In this paper, we study a hydrodynamic system modeling the deformation of vesicle membranes in incompressible viscous fluids. The system consists of the Navier-Stokes equations cou…
On the General Ericksen-Leslie System: Parodi's Relation, Well-posedness and Stability
Hao Wu, Xiang Xu, Chun Liu
In this paper we investigate the role of Parodi's relation in the well-posedness and stability of the general Ericksen-Leslie system modeling nematic liquid crystal flows. First, w…
Asymptotic Behavior for a Nematic Liquid Crystal Model with Different Kinematic Transport Properties
Hao Wu, Xiang Xu, Chun Liu
We study the asymptotic behavior of global solutions to hydrodynamical systems modeling the nematic liquid crystal flows under kinematic transports for molecules of different shape…