Fanghua Lin

Q: What Schools Are Affiliated With Fanghua Lin

Fanghua Lin is affiliated with the following schools: National Cheng Kung University, University of Minnesota, Princeton University, University of Chicago, Stanford University, Zhejiang University, New York University

Fanghua Lin's AcademicInfluence.com Rankings

Fanghua Lin

Mathematics

#2704

World Rank

#4120

Historical Rank

#1053

USA Rank

Measure Theory

#875

World Rank

#1149

Historical Rank

#327

USA Rank

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Mathematics

Fanghua Lin's Degrees

Masters Mathematics Stanford University

Why Is Fanghua Lin Influential?

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According to Wikipedia, Fanghua Lin , also written as Fang-Hua Lin, is a Chinese-born American mathematician. He is currently the Silver Professor at the Courant Institute of Mathematical Sciences at New York University. He applies rigorous analysis to nonlinear systems and is a leader in this field.

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Fanghua Lin's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Nonparabolic dissipative systems modeling the flow of liquid crystals (1995) (618)
A new proof of the Caffarelli‐Kohn‐Nirenberg theorem (1998) (543)
Monotonicity properties of variational integrals, ap weights and unique continuation (1986) (415)
Nonlinear theory of defects in nematic liquid crystals; Phase transition and flow phenomena (1989) (414)
On hydrodynamics of viscoelastic fluids (2005) (366)
Compactness methods in the theory of homogenization (1987) (362)
Existence and partial regularity of static liquid crystal configurations (1986) (344)
Unique continuation for elliptic operators: A geometric‐variational approach (1987) (334)
Liquid Crystal Flows in Two Dimensions (2010) (331)
Elliptic Partial Differential Equations (2000) (292)
Existence of Solutions for the Ericksen-Leslie System (2000) (282)
Partial regularity of the dynamic system modeling the flow of liquid crystals (1995) (257)
Mappings minimizing the Lp norm of the gradient (1987) (245)
Nodal sets of solutions of elliptic and parabolic equations (1991) (241)
Global small solutions to 2-D incompressible MHD system (2013) (237)
The analysis of harmonic maps and their heat flows (2008) (233)
Some Dynamical Properties of Ginzburg-Landau Vortices (1996) (206)
Convergence Rates in L2 for Elliptic Homogenization Problems (2011) (173)
Global Small Solutions to an MHD‐Type System: The Three‐Dimensional Case (2014) (167)
On the uniqueness of heat flow of harmonic maps and hydrodynamic flow of nematic liquid crystals (2010) (166)
Gradient estimates and blow-up analysis for stationary harmonic maps (1999) (164)
On the initial‐boundary value problem of the incompressible viscoelastic fluid system (2008) (152)
Global Existence of Weak Solutions of the Nematic Liquid Crystal Flow in Dimension Three (2014) (152)
Global mild solutions of Navier‐Stokes equations (2011) (151)
An Optimal Partition Problem for Eigenvalues (2007) (150)
Singularly perturbed elliptic systems and multi-valued harmonic functions with free boundaries (2008) (147)
Homogenization of elliptic systems with Neumann boundary conditions (2010) (143)
Lp bounds on singular integrals in homogenization (1991) (140)
Static and dynamic theories of liquid crystals (2001) (134)
A uniqueness theorem for parabolic equations (1990) (129)
Solutions of perturbed Schrödinger equations with critical nonlinearity (2007) (128)
Recent developments of analysis for hydrodynamic flow of nematic liquid crystals (2014) (128)
Geometric Measure Theory: An Introduction (2010) (125)
On the number of interior peak solutions for a singularly perturbed Neumann problem (2007) (115)
Topology of sobolev mappings, II (2003) (113)
Complex Ginzburg-Landau equations in high dimensions and codimension two area minimizing currents (1999) (112)
Regularity of an elliptic problem with a singular nonlinearity (1993) (112)
Topology of Sobolev mappings (2001) (110)
Energy identity of harmonic map flows from surfaces at finite singular time (1998) (109)
Ginzburg-Landau vortices: dynamics, pinning, and hysteresis (1997) (108)
On the Incompressible Fluid Limit and the Vortex Motion Law of the Nonlinear Schrödinger Equation (1999) (106)
Some Analytical Issues for Elastic Complex Fluids (2012) (105)
Harmonic and quasi-harmonic spheres (1999) (105)
Periodic Homogenization of Green and Neumann Functions (2014) (99)
On a micro‐macro model for polymeric fluids near equilibrium (2007) (98)
Complex Ginzburg-Landau equations and dynamics of vortices, filaments, and codimension-2 submanifolds (1998) (95)
On the Dirichlet problem for minimal graphs in hyperbolic space (1989) (94)
Stable defects of minimizers of constrained variational principles (1988) (93)
Geometric measure of singular sets of elliptic equations (1998) (90)
On nematic liquid crystals with variable degree of orientation (1991) (90)
On the hydrodynamic limit of Ginzburg-Landau vortices (1999) (89)
Compactness methods in the theory of homogenization II: Equations in non‐divergence form (1989) (84)
Evolution of harmonic maps with Dirichlet boundary conditions (1993) (82)
On the Global Existence of Smooth Solution to the 2-D FENE Dumbbell Model (2007) (82)
A quantization property for static Ginzburg-Landau vortices (2001) (77)
A remark on H1 mappings (1986) (77)
Regularity and Existence of Global Solutions to the Ericksen–Leslie System in $${\mathbb{R}^2}$$R2 (2013) (76)
Regularity and Existence of Global Solutions to the Ericksen–Leslie System in R2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{d (2014) (71)
Homogenization of elliptic problems withLp boundary data (1987) (68)
Second derivative Lp-estimates for elliptic equations of nondivergent type (1986) (68)
A remark on the map x/[x] (1987) (65)
Global Existence for Two Dimensional Incompressible Magnetohydrodynamic Flows with Zero Magnetic Diffusivity (2014) (64)
Global Solutions of Two‐Dimensional Incompressible Viscoelastic Flows with Discontinuous Initial Data (2013) (64)
Solutions of Ginzburg-Landau equations and critical points of the renormalized energy (1995) (63)
Energy quantization for harmonic maps (2002) (62)
The geometry of solutions to a segregation problem for nondivergence systems (2009) (61)
Regularity at infinity for area-minimizing hypersurfaces in hyperbolic space (1987) (56)
Finite Time Singularity of the Nematic Liquid Crystal Flow in Dimension Three (2015) (55)
Global Small Solutions to a Complex Fluid Model in Three Dimensional (2014) (50)
Structure of Helicity and Global Solutions of Incompressible Navier–Stokes Equation (2015) (48)
Axially symmetric harmonic maps minimizing a relaxed energy (1992) (47)
Static Theory for Planar Ferromagnets and Antiferromagnets (2001) (47)
Semiclassical Limit of the Gross-Pitaevskii Equation in an Exterior Domain (2006) (47)
Nonlocal heat flows preserving the L2 energy (2008) (44)
The Variety of Configurations of Static Liquid Crystals (1990) (43)
Traveling wave solutions of the Schrödinger map equation (2010) (41)
Nodal sets of solutions of parabolic equations: II (1994) (41)
Time Evolution of Nematic Liquid Crystals with Variable Degree of Orientation (2002) (38)
Nodal sets of Steklov eigenfunctions (2014) (38)
On the Two‐Dimensional Muskat Problem with Monotone Large Initial Data (2016) (37)
Regularity for Shape Optimizers: The Nondegenerate Case (2016) (36)
A partial answer to a conjecture of B. Simon concerning unique continuation (1990) (36)
Stability of singularities of minimizing harmonic maps (1989) (36)
Estimates of eigenvalues and eigenfunctions in periodic homogenization (2012) (36)
Minimax solutions of the Ginzburg-Landau equations (1997) (36)
Harmonic and quasi-harmonic spheres, part II (2002) (36)
Partially constrained boundary conditions with energy minimizing mappings (1989) (35)
ZERO SET OF SOBOLEV FUNCTIONS WITH NEGATIVE POWER OF INTEGRABILITY (2004) (34)
Singularities for p-energy minimizing unit vectorfields on planar domains (1995) (33)
A Quantization Property for Moving Line Vortices (2001) (33)
Variational problems with free interfaces (1993) (33)
Vortex dynamics for the nonlinear wave equation (1999) (33)
Analysis on singular spaces (1997) (32)
Asymptotic behavior of area-minimizing currents in hyperbolic space (1989) (32)
Strong convergence of p-harmonic mappings (1994) (31)
A REMARK ON THE JACOBIANS (2000) (30)
Homogenization of Poisson's kernal and applications to boundary control (1989) (30)
On Ancient Solutions of the Heat Equation (2017) (29)
Magnetic Field-Induced Instabilities in Liquid Crystals (2007) (28)
Boundary C1,α regularity for variational inequalities (1991) (28)
A remark on the previous paper “Some dynamical properties of Ginzburg-Landau vortices” (1996) (28)
On the Elliptic Equation D i [ a ij (x)D j U ] - k(x)U + K(x)U p = 0 (1985) (28)
On the geometric measure of nodal sets of solutions (1994) (27)
Harmonic maps into round cones and singularities of nematic liquid crystals (1993) (27)
Legendrian energy minimizers. Part I: Heisenberg group target (2001) (27)
Static and moving vortices in Ginzburg-Landau theories (1997) (26)
Vanishing Viscosity Limit for Incompressible Viscoelasticity in Two Dimensions (2017) (25)
The singular set of an energy minimizing map fromB4 toS2 (1990) (25)
Numerical approximations of a norm-preserving gradient flow and applications to an optimal partition problem (2008) (25)
A generalization of Eells-Sampson's theorem (1992) (25)
On the elliptic equation ᵢ[ᵢⱼ()ⱼ]-()+()^{}=0 (1985) (25)
PARTIAL REGULARITY FOR OPTIMAL DESIGN PROBLEMS INVOLVING BOTH BULK AND SURFACE ENERGIES (1999) (24)
Topology of Sobolev mappings III (2003) (24)
Stable Stationary Harmonic Maps to Spheres (2006) (23)
Singularities of p‐energy minimizing maps (1997) (21)
Un theoreme de Liouville pour des equation elliptiques a coefficient periodiques (French): [A Liouville theorem for elliptic equations with peridic coefficients] (1989) (21)
Partial regularity for weak heat flows into spheres (2010) (20)
Harmonic and quasi-harmonic spheres, part III. Rectifiablity of the parabolic defect measure and generalized varifold flows (2002) (20)
A class of fully nonlinear elliptic equations with singularity at the boundary (1998) (20)
Phase transition for potentials of high‐dimensional wells (2012) (20)
Finite Time Blowup for the Nematic Liquid Crystal Flow in Dimension Two (2019) (19)
Mapping Problems � Fundamental Groups and Defect Measures (2003) (19)
Global solutions of the evolutionary Faddeev model with small initial data (2011) (19)
Asymptotically conic elliptic operators and Liouville type theorems (1996) (18)
Solvability of the Stokes Immersed Boundary Problem in Two Dimensions (2017) (18)
Analysis on the junctions of domain walls (2010) (18)
On Ericksen’s model for liquid crystals (1994) (18)
The FENE dumbbell model near equilibrium (2008) (17)
Regularity for Shape Optimizers: The Degenerate Case (2019) (17)
Mixed vortex-antivortex solutions of Ginzburg-Landau equations (1995) (17)
Mapping problems, fundamental groups and defect measures (1999) (16)
Simulation of Natural Convection in a Vertical Enclosure by Using a New Incompressible Flow Formulation - Pseudovorticity-Velocity Formulation (1997) (16)
Multiplicity of solutions for a noncooperative elliptic system with critical Sobolev exponent (2009) (14)
Riesz transform under perturbations via heat kernel regularity (2018) (13)
Nodal Sets and Doubling Conditions in Elliptic Homogenization (2018) (13)
Minimality and stability of minimal hypersurfaces in IRn (1987) (13)
The $p$-energy minimality of $x / \lvert x \rvert$ (1998) (12)
Singular Sets of Higher Order Elliptic Equations (2003) (12)
Numerical Simulation of Three-Dimensional Incompressible Flow by a New Formulation (1996) (11)
Vortices in p-Wave Superconductivity (2003) (11)
Remarks on approximate harmonic maps (1995) (11)
Defects of liquid crystals with variable degree of orientation (2016) (11)
Automatic quadrilateral mesh generation and quality improvement techniques for an improved combination method (2015) (11)
Vortex State of d-Wave Superconductors in the Ginzburg-Landau Energy (2000) (10)
On the Cauchy problem for two dimensional incompressible viscoelastic flows (2016) (10)
The Best Hölder Exponent for Solutions of the Non-parametric Least Area Problem (1985) (10)
On nematic liquid crystal droplets (1996) (9)
Evolution equations with a free boundary condition (1998) (9)
On the hydrodynamic limit of Ginzburg‐Landau wave vortices (2002) (9)
Extremum problems of Laplacian eigenvalues and generalized Polya conjecture (2017) (9)
Lectures on the Analysis of Nonlinear Partial Differential Equations (2018) (8)
Equations for viscoelastic fluids (2018) (8)
On the isometric embedding of torus in R3 (2008) (8)
Varifold type theory for Sobolev mappings (2001) (8)
Erratum: On the Dirichlet problem for minimal graphs in hyperbolic space (2012) (8)
Regularity and Existence of Global Solutions to the Ericksen–Leslie System in R 2 (2014) (8)
Exponential growth solutions of elliptic equations (1999) (8)
Static and moving defects in liquid crystals (1991) (8)
Nematic Liquid Crystals with Variable Degree of Orientation (1991) (8)
On a Mushy Cell Tracking Method for Simulating Gallium Melting (2007) (7)
Isotropic‐Nematic Phase Transition and Liquid Crystal Droplets (2020) (7)
Homogenization of Green and Neumann Functions (2012) (7)
Topology of sobolev mappings IV (2005) (7)
Remarks on a backward parabolic problem (2003) (7)
On Current Developments in Partial Differential Equations (2020) (7)
Plateau's problem for H-convex curves (1987) (7)
Estimates for surfaces which are stationary for an elliptic parametric integral (1990) (7)
Approximation by smooth embedded hypersurfaces with positive mean curvature (1987) (7)
Rank Zero and Rank One Sets of Harmonic Maps (2000) (7)
Counterexamples related to high-frequency oscillation of Poisson's kernel (1987) (6)
A Lioville Type Theorem for Minimizing Maps (2002) (6)
A remark about the stability of smooth equilibrium configurations of static liquid crystals (1986) (6)
Solutions of Ginzburg-Landau equations and critical points of the renormalized energy (2018) (6)
Behaviour of nonparametric solutions and free boundary regularity (1987) (6)
On the viscous Camassa-Holm equations with fractional diffusion (2017) (6)
Matrix-valued Allen–Cahn equation and the Keller–Rubinstein–Sternberg problem (2021) (6)
Upper bounds of nodal sets for eigenfunctions of eigenvalue problems (2020) (5)
Tangential regularity near the C1-boundary (1986) (5)
Engineering applications of 2D and 3D finite element mesh generation in hydrogeology and water resources (2017) (5)
On the Betti numbers of level sets of solutions to elliptic equations (2016) (5)
Semiclassical states of Hamiltonian system of Schrodinger equations with subcritical nonlinearities (2006) (5)
Fonctions quasi affines et minimisation de ⌈⌈∇μlp (French): [Null-Lagrangians and the minimization of ⌈⌈∇μlp] (1988) (4)
A New Type of Free Boundary Problem with Volume Constraint (2004) (4)
Rectifiability of defect measures, fundamental groups and density of Sobolev mappings (1996) (4)
Non-minimality of Minimal Graphs (1987) (4)
Uniqueness and nonuniqueness of the plateau problem (1987) (4)
Soliton dynamics in planar ferromagnets and anti-ferromagnets. (2003) (4)
Uniform boundary controllability and homogenization of wave equations (2019) (4)
Harmonic Maps in Connection of Phase Transitions with Higher Dimensional Potential Wells (2018) (4)
On regularity and singularity of free boundaries in obstacle problems (2009) (4)
Existence of Faddeev knots (2008) (4)
Large m asymptotics for minimal partitions of the Dirichlet eigenvalue (2020) (4)
On the least growth of harmonic functions and the boundary behavior of riemann mappings (1985) (4)
The dynamical law of Ginzburg-Landau vortices (1995) (3)
Existence and regularity of embedded disks (1988) (3)
Complexity of solutions of partial differential equations (2008) (3)
Boundary behavior of solutions of area‐type problems (1988) (3)
Existence of Faddeev knots in general Hopf dimensions (2009) (3)
Multiple Time Scale Dynamics in Coupled Ginzburg-Landau Equations (2003) (3)
Scaling limit for compressible viscoelastic fluids (2014) (2)
Boundary Harnack principle on nodal domains (2021) (2)
Existence et regularite des configurations statiques des cristaux liquides (French): [Existence and smoothness of static liquid crystal configurations] (1985) (2)
Methodes de compacite en homogeneisation (French): [Compactness methods in the theory of homogenization] (1987) (2)
An Automatic Method for Complete Triangular Mesh Conversion into Quadrilateral Mesh for Multiple Domain Geometry (2016) (2)
MULTIGRID SOLUTIONS OF THE EULER AND NAVIER-STOKES EQUATIONS ON UNSTRUCTURED GRIDS (1999) (2)
Vortices in two-dimensional Bose-Einstein condensates (2002) (1)
SKYRMIONS IN GROSS-PITAEVSKII FUNCTIONALS (2009) (1)
An Automatic Delaunay Triangular Mesh Generation Method based On Point Spacing (2013) (1)
Critical Sets of Solutions of Elliptic Equations in Periodic Homogenization (2022) (1)
Mixed convective heating of a moving plate in a parallel duct (1993) (1)
Micro-genetic approach for surface meshing on a set of unorganized points (2007) (1)
Erratum: Geometric measure of singular sets of elliptic equations (1999) (1)
Revisit the regularity theory of Navier-Stokes equation (1)
A type of homogenization problem (2002) (1)
Dynamics of Ginzburg-Landau vortices: The pinning effect (1996) (1)
Introduction to harmonic maps (2008) (1)
Liquid crystal droplets and free interfaces (1995) (1)
Geometric measure of nodal and growth of solutions to elliptic equations (1998) (1)
Some Recent Trends of Nonlinear Partial Differential Equations (1)
Critical Sets of Elliptic Equations with Rapidly Oscillating Coefficients in Two Dimensions (2022) (1)
Superfluids passing an obstacle and vortex nucleation (2018) (1)
Erratum to “Uniform boundary controllability and homogenization of wave equations” (2022) (0)
Convergence Rates in L2 for Elliptic Homogenization Problems (2011) (0)
Structure of Helicity and Global Solutions of Incompressible Navier–Stokes Equation (2015) (0)
An eigenvalue problem on negativity curved manifolds (1991) (0)
Global Small Solutions to a Complex Fluid Model in Three Dimensional (2014) (0)
Bubbling and quantization in high dimensions (2003) (0)
Topology of Sobolev mappings and associated variational problems (2011) (0)
6 th Symposium on Analysis and PDEs Purdue University , June 1 – 4 , 2015 ABSTRACTS Principal Lecturers (2015) (0)
Complex Ginzburg-landau Equations in High Dimensions and Codimension Two Area Minimizing Currents. Part Ii : a Proof of the Eta-compactness in Dimension N > 3 (2007) (0)
A pr 2 01 8 SUPERFLUIDS PASSING AN OBSTACLE AND VORTEX NUCLEATION (2018) (0)
On the 2D Muskat Problem with Monotone Large Initial Data (2016) (0)
Defects in Liquid Crystal Flows (2022) (0)
SKYRMIONS IN GROSS-PITAEVSKII (2009) (0)
Weak solutions, part II (2000) (0)
Bubbling analysis in dimension two (2008) (0)
Complex Ginzburg-landau Equations in High Dimensions and Codimension Two Area Minimizing Currents. Part I: the Dimension Three Case (2007) (0)
On the Incompressible Fluid Limit andthe Vortex Motion Law of theNonlinear Schr (2009) (0)
Semiclassical limit of the cubic nonlinear Schodinger equation concerning a superfluid passing obstacle: Seminaire: Equations aux derivees partielles 2004-2005 (2005) (0)
Upper bounds of nodal sets for eigenfunctions of eigenvalue problems (2020) (0)
Nematic Liquid Crystal Flow with Partially Free Boundary (2022) (0)
Dynamics of defect measures in heat flows (2008) (0)
Semiclassical Limit of the cubic nonlinear Schrödinger Equation concerning a superfluid passing an obstacle (2005) (0)
Defects of liquid crystals with variable degree of orientation (2017) (0)
Rectifiability of defect measures, fundamental groups and density of Sobolev mappings (2018) (0)
The Characterization of Orthogonal Affine Bivariate Pseudoframes (2010) (0)
A density-controlled triangular and quadrilateral element mesh automatic generation system (2013) (0)
Rectifiability of defect measures, fundamental groups and density of Sobolev mappings (2018) (0)
Blow up analysis on heat flows (2008) (0)
Nodal sets of Steklov eigenfunctions (2015) (0)
ON THE BETTI NUMBERS OF NODAL SETS OF THE ELLIPTIC EQUATIONS (2013) (0)
Partially smooth heat flows (2008) (0)
Mapping Problems , Fundamental Groupsand Defect (1998) (0)
DATA WAREHOUSING AND MESHING FOR LARGE SCALE DATASET FROM SURVEYED PROFILES OF WATERCOURSES (2003) (0)
Nonlinear partial differential equations : proceedings of international conference, Zhejiang University, June 1992 (1993) (0)
Louis Nirenberg (1925–2020) (2021) (0)
Riesz transform on exterior Lipschitz domains (2022) (0)
Blow up analysis of stationary harmonic maps (2008) (0)
Regularity of minimizing harmonic maps (2008) (0)
Regularity of stationary harmonic maps (2008) (0)
Singular Sets of Energy Minimizing Maps (1991) (0)
SKYRMIONS IN GROSS-PITAEVSKII FUNCTIONALS ∗ Dedicated to Professor Wu Wenjun on the occasion of his 90 th birthday (2009) (0)
Nodal Sets and Doubling Conditions in Elliptic Homogenization (2019) (0)
From the SelectedWorks of Yi Li August 1 , 1991 Boundary C 1 , α Regularity for Variational Inequalities (2017) (0)
Revolution, Transitions, Partial Differential Equations (2010) (0)
Finite Time Singularity of the Nematic Liquid Crystal Flow in Dimension Three (2016) (0)
Some recent results on harmonic maps to spheres (1993) (0)
Revisit the topology of Sobolev maps (2004) (0)
On the convergence of a class of quadratic interpolation splines (Chinese) (1981) (0)
Heat flows to Riemannian manifolds of NPC (2008) (0)
Applying Spectra Analysis to Estimate the Hydraulic Diffusivity of Aquifers - A Case Study of the Apex of Chou Shui Alluvial Fan (2011) (0)

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