Simple finite element method in vorticity formulation for incompressible flows. - Jian-Guo Liu 006; Weinan E (Math. Comput., 2001)

Convergence of the point vortex method for 2-D vortex sheet. - Jian-Guo Liu 006; Zhouping Xin (Math. Comput., 2001)

Projection method III: Spatial discretization on the staggered grid. - Weinan E; Jian-Guo Liu 006 (Math. Comput., 2002)

Analysis of finite difference schemes for unsteady Navier-Stokes equations in vorticity formulation. - Cheng Wang 015; Jian-Guo Liu 006 (Numerische Mathematik, 2002)

Concepts and Application of Time-Limiters to High Resolution Schemes. - Karthikeyan Duraisamy; James D. Baeder; Jian-Guo Liu 006 (J. Sci. Comput., 2003)

A Fourth Order Scheme for Incompressible Boussinesq Equations. - Jian-Guo Liu 006; Cheng Wang 015; Hans Johnston (J. Sci. Comput., 2003)

Epitaxial Growth Without Slope Selection: Energetics, Coarsening, and Dynamic Scaling. - Bo Li 007; Jian-Guo Liu 006 (J. Nonlinear Sci., 2004)

Analysis of a fourth order finite difference method for the incompressible Boussinesq equations. - Cheng Wang 015; Jian-Guo Liu 006; Hans Johnston (Numerische Mathematik, 2004)

Macroscopic Fluid Models with Localized Kinetic Upscaling Effects. - Pierre Degond; Jian-Guo Liu 006; Luc Mieussens (Multiscale Model. Simul., 2006)

Convergence Analysis of the Energy and Helicity Preserving Scheme for Axisymmetric Flows. - Jian-Guo Liu 006; Wei-Cheng Wang (SIAM J. Numer. Anal., 2006)

Analysis of a sequential regularization method for the unsteady Navier-Stokes equations. - Xiliang Lu; Ping Lin 001; Jian-Guo Liu 006 (Math. Comput., 2008)

Analysis of an Asymptotic Preserving Scheme for the Euler-Poisson System in the Quasineutral Limit. - Pierre Degond; Jian-Guo Liu 006; Marie Hélène Vignal (SIAM J. Numer. Anal., 2008)

Long Time Numerical Solution of the Navier–Stokes Equations Based on a Sequential Regularization Formulation. - Ping Lin 001; Jian-Guo Liu 006; Xiliang Lu (SIAM J. Sci. Comput., 2008)

Characterization and Regularity for Axisymmetric Solenoidal Vector Fields with Application to Navier-Stokes Equation. - Jian-Guo Liu 006; Wei-Cheng Wang (SIAM J. Math. Anal., 2009)

Stable and accurate pressure approximation for unsteady incompressible viscous flow. - Jian-Guo Liu 006; Jie Liu 003; Robert L. Pego (J. Comput. Phys., 2010)

Analysis of an Asymptotic Preserving Scheme for Linear Kinetic Equations in the Diffusion Limit. - Jian-Guo Liu 006; Luc Mieussens (SIAM J. Numer. Anal., 2010)

Two nonlinear compactness theorems in Lp(0, T;B). - Xiuqing Chen; Jian-Guo Liu 006 (Appl. Math. Lett., 2012)

Multidimensional Degenerate Keller-Segel System with Critical Diffusion Exponent 2n/(n+2). - Li Chen; Jian-Guo Liu 006; Jinhuan Wang (SIAM J. Math. Anal., 2012)

Dynamics in a Kinetic Model of Oriented Particles with Phase Transition. - Amic Frouvelle; Jian-Guo Liu 006 (SIAM J. Math. Anal., 2012)

Convergence of a Particle Method and Global Weak Solutions of a Family of Evolutionary PDEs. - Alina Chertock; Jian-Guo Liu 006; Terrance Pendleton (SIAM J. Numer. Anal., 2012)

Asymptotic-preserving schemes for kinetic-fluid modeling of disperse two-phase flows. - Thierry Goudon; Shi Jin 003; Jian-Guo Liu 006; Bokai Yan (J. Comput. Phys., 2013)

Macroscopic Limits and Phase Transition in a System of Self-propelled Particles. - Pierre Degond; Amic Frouvelle; Jian-Guo Liu 006 (J. Nonlinear Sci., 2013)

A domain decomposition method for semilinear hyperbolic systems with two-scale relaxations. - Shi Jin 003; Jian-Guo Liu 006; Li Wang 020 (Math. Comput., 2013)

Analysis of Polymeric Flow Models and Related Compactness Theorems in Weighted Spaces. - Xiuqing Chen; Jian-Guo Liu 006 (SIAM J. Math. Anal., 2013)

A Generalized MAC Scheme on Curvilinear Domains. - Yin-Liang Huang; Jian-Guo Liu 006; Wei-Cheng Wang (SIAM J. Sci. Comput., 2013)

Large-Scale Dynamics of Mean-Field Games Driven by Local Nash Equilibria. - Pierre Degond; Jian-Guo Liu 006; Christian A. Ringhofer (J. Nonlinear Sci., 2014)

A Local Pressure Boundary Condition Spectral Collocation Scheme for the Three-Dimensional Navier-Stokes Equations. - Hans Johnston; Cheng Wang 015; Jian-Guo Liu 006 (J. Sci. Comput., 2014)

Flow on Sweeping Networks. - Pierre Degond; Michael Herty; Jian-Guo Liu 006 (Multiscale Model. Simul., 2014)

Simple Finite Element Numerical Simulation of Incompressible Flow Over Non-rectangular Domains and the Super-Convergence Analysis. - Yunhua Xue; Cheng Wang 015; Jian-Guo Liu 006 (J. Sci. Comput., 2015)

An Exact Solution for Stokes Flow in a Channel with Arbitrarily Large Wall Permeability. - Gregory J. Herschlag; Jian-Guo Liu 006; A. T. Layton (SIAM J. Appl. Math., 2015)

A note on Monge-Ampère Keller-Segel equation. - Hui Huang; Jian-Guo Liu 006 (Appl. Math. Lett., 2016)

Refined hyper-contractivity and uniqueness for the Keller-Segel equations. - Jian-Guo Liu 006; Jinhuan Wang (Appl. Math. Lett., 2016)

On a Schrödinger-Landau-Lifshitz System: Variational Structure and Numerical Methods. - Jingrun Chen; Jian-Guo Liu 006; Zhennan Zhou (Multiscale Model. Simul., 2016)

Existence Theorems for a Multidimensional Crystal Surface Model. - Jian-Guo Liu 006; Xiangsheng Xu (SIAM J. Math. Anal., 2016)

Batch Size Matters: A Diffusion Approximation Framework on Nonconvex Stochastic Gradient Descent. - Chris Junchi Li; Lei Li 006; Junyang Qian; Jian-Guo Liu 006 (CoRR, 2017)

A Modified Levy Jump-Diffusion Model Based on Market Sentiment Memory for Online Jump Prediction. - Zheqing Zhu; Jian-Guo Liu 006; Lei Li 006 (CoRR, 2017)

Coagulation-Fragmentation Model for Animal Group-Size Statistics. - Pierre Degond; Jian-Guo Liu 006; Robert L. Pego (J. Nonlinear Sci., 2017)

Continuum Limit of a Mesoscopic Model with Elasticity of Step Motion on Vicinal Surfaces. - Yuan Gao 004; Jian-Guo Liu 006; Jianfeng Lu 001 (J. Nonlinear Sci., 2017)

Explicit and Implicit TVD Schemes for Conservation Laws with Caputo Derivatives. - Jian-Guo Liu 006; Zheng Ma 010; Zhennan Zhou (J. Sci. Comput., 2017)

Error estimate of a random particle blob method for the Keller-Segel equation. - Hui Huang; Jian-Guo Liu 006 (Math. Comput., 2017)

A random particle blob method for the Keller-Segel equation and convergence analysis. - Jian-Guo Liu 006; Rong Yang (Math. Comput., 2017)

Global Convergence of a Sticky Particle Method for the Modified Camassa-Holm Equation. - Yu Gao; Jian-Guo Liu 006 (SIAM J. Math. Anal., 2017)

Weak Solution of a Continuum Model For Vicinal Surface in The Attachment-Detachment-Limited Regime. - Yuan Gao 004; Jian-Guo Liu 006; Jianfeng Lu 001 (SIAM J. Math. Anal., 2017)

Analytical Validation of a Continuum Model for the Evolution of a Crystal Surface in Multiple Space Dimensions. - Jian-Guo Liu 006; Xiangsheng Xu (SIAM J. Math. Anal., 2017)

A note on one-dimensional time fractional ODEs. - Yuanyuan Feng; Lei Li 006; Jian-Guo Liu 006; Xiaoqian Xu (Appl. Math. Lett., 2018)

An accurate front capturing scheme for tumor growth models with a free boundary limit. - Jian-Guo Liu 006; Min Tang 002; Li Wang 101; Zhennan Zhou (J. Comput. Phys., 2018)

Entropic sub-cell shock capturing schemes via Jin-Xin relaxation and Glimm front sampling for scalar conservation laws. - Frédéric Coquel; Shi Jin 003; Jian-Guo Liu 006; Li Wang 020 (Math. Comput., 2018)

Positivity-preserving and asymptotic preserving method for 2D Keller-Segal equations. - Jian-Guo Liu 006; Li Wang; Zhennan Zhou (Math. Comput., 2018)

A Dispersive Regularization for the Modified Camassa-Holm Equation. - Yu Gao; Lei Li 006; Jian-Guo Liu 006 (SIAM J. Math. Anal., 2018)

A Generalized Definition of Caputo Derivatives and Its Application to Fractional ODEs. - Lei Li 006; Jian-Guo Liu 006 (SIAM J. Math. Anal., 2018)

Some Compactness Criteria for Weak Solutions of Time Fractional PDEs. - Lei Li 006; Jian-Guo Liu 006 (SIAM J. Math. Anal., 2018)

Uniform-in-Time Weak Error Analysis for Stochastic Gradient Descent Algorithms via Diffusion Approximation. - Yuanyuan Feng; Tingran Gao; Lei Li 006; Jian-Guo Liu 006; Yulong Lu (CoRR, 2019)

A stochastic version of Stein Variational Gradient Descent for efficient sampling. - Lei Li 006; Jian-Guo Liu 006; Zibu Liu; Jianfeng Lu 001 (CoRR, 2019)

Towards understanding the boundary propagation speeds in tumor growth models. - Jian-Guo Liu 006; Min Tang 002; Li Wang 101; Zhennan Zhou (CoRR, 2019)

Field model for complex ionic fluids: analytical properties and numerical investigation. - Jian-Guo Liu 006; Jinhuan Wang; Zhennan Zhou; Yu Zhao (CoRR, 2019)

A Discretization of Caputo Derivatives with Application to Time Fractional SDEs and Gradient Flows. - Lei Li 006; Jian-Guo Liu 006 (SIAM J. Numer. Anal., 2019)

Complete-Q Model for Poro-Viscoelastic Media in Subsurface Sensing: Large-Scale Simulation With an Adaptive DG Algorithm. - Qiwei Zhan; Mingwei Zhuang; Zhennan Zhou; Jian-Guo Liu 006; Qing Huo Liu (IEEE Trans. Geosci. Remote. Sens., 2019)

A direct simulation approach for the Poisson-Boltzmann equation using the Random Batch Method. - Lei Li 006; Jian-Guo Liu 006; Yijia Tang (CoRR, 2020)

A Proximal-Gradient Algorithm for Crystal Surface Evolution. - Katy Craig; Jian-Guo Liu 006; Jianfeng Lu 001; Jeremy Louis Marzuola; Li Wang 036 (CoRR, 2020)

Random Batch Methods (RBM) for interacting particle systems. - Shi Jin 003; Lei Li 006; Jian-Guo Liu 006 (J. Comput. Phys., 2020)

Large time behaviors of upwind schemes and B-schemes for Fokker-Planck equations on ℝ by jump processes. - Lei Li 006; Jian-Guo Liu 006 (Math. Comput., 2020)

A structure preserving numerical scheme for Fokker-Planck equations of neuron networks: Numerical analysis and exploration. - Jingwei Hu; Jian-Guo Liu 006; Yantong Xie; Zhennan Zhou (J. Comput. Phys., 2021)

Toward Understanding the Boundary Propagation Speeds in Tumor Growth Models. - Jian-Guo Liu 006; Min Tang 002; Li Wang 101; Zhennan Zhou (SIAM J. Appl. Math., 2021)

Convergence of the Random Batch Method for Interacting Particles with Disparate Species and Weights. - Shi Jin 003; Lei Li 006; Jian-Guo Liu 006 (SIAM J. Numer. Anal., 2021)

A proximal-gradient algorithm for crystal surface evolution. - Katy Craig; Jian-Guo Liu 006; Jianfeng Lu 001; Jeremy Louis Marzuola; Li Wang 101 (Numerische Mathematik, 2022)

Projection Method for Droplet Dynamics on Groove-Textured Surface with Merging and Splitting. - Yuan Gao 004; Jian-Guo Liu 006 (SIAM J. Sci. Comput., 2022)

Diffusion approximations of Oja's online principal component analysis. - Jian-Guo Liu 006; Zibu Liu (CoRR, 2023)

High-order Moment Closure Models with Random Batch Method for Efficient Computation of Multiscale Turbulent Systems. - Di Qi; Jian-Guo Liu 006 (CoRR, 2023)

On the dynamics of the boundary vorticity for incompressible viscous flows. - Vladislav Cherepanov; Jian-Guo Liu 006; Z. Qian (CoRR, 2023)

A Selection Principle for Weak KAM Solutions via Freidlin-Wentzell Large Deviation Principle of Invariant Measures. - Yuan Gao 004; Jian-Guo Liu 006 (SIAM J. Math. Anal., 2023)

A Three-dimensional tumor growth model and its boundary instability. - Jian-Guo Liu 006; Thomas Witelski; Xiaoqian Xu; Jiaqi Zhang (CoRR, 2024)

Some Grönwall Inequalities for a Class of Discretizations of Time Fractional Equations on Nonuniform Meshes. - Yuanyuan Feng; Lei Li 006; Jian-Guo Liu 006; Tao Tang (SIAM J. Numer. Anal., 2024)

On the Dynamics of the Boundary Vorticity for Incompressible Viscous Flows. - Vladislav Cherepanov; Jian-Guo Liu 006; Zhongmin Qian (J. Sci. Comput., 2024)

A Simple Construction of Fat Cantor Sets. - Jian-Guo Liu 006; Robert L. Pego (Am. Math. Mon., 2024)

Oscillatory solutions at the continuum limit of Lorenz 96 systems. - Jian-Guo Liu 006; Di Qi (Commun. Inf. Syst., 2025)

Data Assimilation Models for Computing Probability Distributions of Complex Multiscale Systems. - Di Qi; Jian-Guo Liu 006 (CoRR, 2025)