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Acta Mathematica Scientia 2024年第1期44卷 195-214页

作者：丁时进李颖花王喻 School of Mathematical Sciences South China Normal UniversityGuangzhou510631China

This paper is concerned with the Navier-Stokes/Allen-Cahn system,which is used to model the dynamics of immiscible two-phase *** consider a 1D free boundary problem and assume that the viscosity coefficient depends on the density in the form ofη(ρ)=ρ^(α).The existence of unique global H^(2m)-solutions(m∈N)to the free boundary problem is proven for when 0<α<1/***,we obtain the global C^(∞)-solutions if the initial data is smooth.

关键词： Navier-Stokes/Allen-Cahn system density-dependent viscosity free boundary global solutions

Spherically Symmetric Solutions to Compressible Hydrodynamic Flow of Liquid Crystals in N Dimensions

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Chinese Annals of Mathematics,Series B 2012年第3期33卷 453-478页

作者： Jinrui HUANG shijin ding School of Mathematical Sciences South China Normal UniversityGuangzhou 510631China

The paper is concerned with the system modeling the compressible hydrodynamic flow of liquid crystals with radially symmetric initial data and non-negative initial density in dimension N(N ≥ 2).The authors obtain the... 详细信息

关键词： Liquid crystals Compressible hydrodynamic flow Global solutions

Global well-posedness for the dynamical Q-tensor model of liquid crystals

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Science China Mathematics 2015年第6期58卷 1349-1366页

作者： HUANG JinRui ding shijin School of Mathematics and Computational Science Wuyi University School of Mathematical Sciences South China Normal University

We consider a complex fluid modeling nematic liquid crystal flows, which is described by a system coupling Navier-Stokes equations with a parabolic Q-tensor system. We first prove the global existence of weak solutions in dimension three. Furthermore, the global well-posedness of strong solutions is studied with sufficiently large viscosity of fluid. Finally, we show a continuous dependence result on the initial data which directly yields the weak-strong uniqueness of solutions.

关键词： dynamical tensor Stokes parabolic nematic viscosity Navier estimates uniqueness proof

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新型显示薄膜喷墨打印技术的数学建模与分析

中国科学：数学 2024年第3期54卷 377-406页

作者：丁时进辛周平王筱平钱铁铮李进开徐新鹏华南师范大学数学科学学院广州510631 香港中文大学数学科学研究所中国香港香港科技大学数学系中国香港香港中文大学(深圳)理工学院深圳518172 深圳市大数据研究院深圳518172 广东以色列理工学院物理系汕头515063

本文将新型显示薄膜喷墨打印技术的关键工艺过程“喷墨打印-干燥/烘烤成膜”中多组分聚合物溶液在压电作用下从喷管内喷出均匀液滴、液滴在基板上着床并融合成均匀的液体薄膜、液体薄膜经过蒸发留下溶质(如有机发光二极管OLED(organic l... 详细信息

本文将新型显示薄膜喷墨打印技术的关键工艺过程“喷墨打印-干燥/烘烤成膜”中多组分聚合物溶液在压电作用下从喷管内喷出均匀液滴、液滴在基板上着床并融合成均匀的液体薄膜、液体薄膜经过蒸发留下溶质(如有机发光二极管OLED(organic light-emitting diode))形成均匀显示薄膜的3个核心科学问题,在数学上提炼为多组分聚合物流体带移动接触线和动态接触角以及带有蒸发条件的固-液-气多相耦合的自由界面问题.本文首先对这些问题的Newton流的数学模型进行热力学自洽的系统综述和完善,然后对包含相分离、溶剂蒸发和非Newton黏弹性等多物理现象的同类自由界面问题进行成体系的数学建模,对模型的理论分析和数值模拟提出一些研究思路.本文希望通过解决这些数学问题突破新型显示薄膜喷墨打印工艺的关键技术瓶颈,提高打印的良品率,推进产业化,促进数学在解决国家重大需求难题中的应用.本文以新型显示薄膜喷墨打印技术核心科学问题为背景,给数学工作者提出了一些新的重要的数学问题,同时也为相关材料科学家提供了可行的数学方案,为双方搭起了良好的沟通桥梁.

关键词：非Newton流喷墨打印液滴动力学液体薄膜蒸发移动接触线和动态接触角自由界面问题

SOLUTIONS OF GINZBURG-LANDAU EQUATIONS WITH WEIGHT AND MINIMIZERS OF THE RENORMALIZED ENERGY

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Applied Mathematics(A Journal of Chinese Universities) 2007年第1期22卷 48-60页

作者： Kou Yanlei ding shijin Department of Mathematics South China Normal University Guangdong 510631~ China.

In this paper, it is proved that for any given d non-degenerate local minimum points of the renormalized energy of weighted Ginzburg-Landau eqautions, one can find solutions to the Ginzburg-Landau equations whose vortices tend to these d points. This provides the connections between solutions of a class of Ginzburg-Landau equations with weight and minimizers of the renormalized energy.

关键词： Ginzburg-Landau equation renormalized energy.

Global existence for slightly compressible hydrodynamic flow of liquid crystals in two dimensions

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Science China Mathematics 2013年第11期56卷 2233-2250页

作者： ding shijin HUANG JinRui LIN JunYu School of Mathematical Sciences South China Normal University Department of Mathematics South China University of Technology

In two dimensions, we study the compressible hydrodynamic flow of liquid crystals with periodic boundary conditions. As shown by ding et al. （2013）, when the parameter λ→∞ oo, the solutions to the compressible liquid crystal system approximate that of the incompressible one. Furthermore, ding et al. （2013） proved that the regular incompressible limit solution is global in time with small enough initial data. In this paper, we show that the solution to the compressible liquid crystal flow also exists for all time, provided that is sufficiently large and the initial data are almost incompressible.

关键词： liquid crystals slightly compressible global existence

GLOBAL EXISTENCE AND DECAY ESTIMATES FOR THE CLASSICAL SOLUTIONS TO A COMPRESSIBLE FLUID-PARTICLE INTERACTION MODEL

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Acta Mathematica Scientia 2019年第6期39卷 1525-1537页

作者： shijin ding Bingyuan HUANG Quanrong LI South China Research Center for Applied Mathematics and Interdisciplinary Studies School of Mathematical SciencesSouth China Normal UniversityGuangzhou 510631China School of Mathematics and Statistics Hanshan Normal UniversityChaozhou 521041China College of Mathematics and Statistics Shenzhen UniversityShenzhen 518060China

We prove the global existence of classical solutions to a fluid-particle interaction model in R^3, namely, compressible Navier-Stokes-Smoluchowski equations, when the initial data are close to the stationary state(ρ*, 0, η*) and the external potential satisfies the smallness assumption. Furthermore, optimal decay rates of classical solutions in H^3-framework are obtained.

关键词： compressible Navier-Stokes-Smoluchowski global classical solutions optimal decay rates

CLASSICAL SOLUTIONS OF THE 3D COMPRESSIBLE FLUID-PARTICLE SYSTEM WITH A MAGNETIC FIELD

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Acta Mathematica Scientia 2022年第4期42卷 1585-1606页

作者： Bingyuan HUANG shijin ding Riqing WU School of Mathematics and Statistics Hanshan Normal UniversityChaozhou521041China South China Research Center for Applied Mathematics and Interdisciplinary Studies School of Mathematical SciencesSouth China Normal University School of Mathematical Sciences South China Normal UniversityGuangzhou 510631 China

This paper addresses the 3-D Cauchy problem of a fluid-particle system with a magnetic ***,the local classical solutions of the linearized model on the sphere Br are obtained by some a priori estimates that do not depend on the radius ***,the classical solutions of the linearized model in R^(3) are obtained by combining the continuation and compactness ***,the classical solutions of the original system are proved by use of the picard iteration argument and the energy method.

关键词： Compressibility fluid-particle system magnetic field classical solution

PINNING　OF　VORTICES　FOR　THE　GINZBURG-LANDAU　FUNCTIONAL　WITH　VARIABLE　COEFFICIENT

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Applied Mathematics:A Journal of Chinese Universities 1997年第1期 79-90页

作者： ding shijin, LIU ZUHAN AND YU WANGHUI

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关键词：

PARTIAL REGULARITY FOR THE 2-DIMENSIONAL WEIGHTED LANDAU-LIFSHITZ FLOW

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Journal of Partial Differential Equations 2007年第1期20卷 11-29页

作者： Ye Yunhua ding shijin Department of Mathematics South China Normal University Guangzhou Guangdong 510631 China

We consider the partial regularity of weak solutions to the weighted Landau-Lifshitz flow on a 2-dimensional bounded smooth domain by Ginzburg-Landau type approximation. Under the energy smallness condition, we prove the uniform local C^∞ bounds for the approaching solutions. This shows that the approximating solutions are locally uniformly bounded in C^∞（Reg（{uε}）∩（Ω^-×R^＋）） which guarantee the smooth convergence in these points. Energy estimates for the approximating equations are used to prove that the singularity set has locally finite two-dimensional parabolic Hausdorff measure and has at most finite points at each fixed time. From the uniform boundedness of approximating solutions in C^∞（Reg（{uε}）∩（Ω^-×R^＋））, we then extract a subsequence converging to a global weak solution to the weighted Landau-Lifshitz flow which is in fact regular away from finitely many points.

关键词： Landau-Lifshitz equations Ginzburg-Landau approximations Hausdorff measure partial regularity.