Publications -- Jian-Guo Liu

Link to publications in chronological order.

Commutator estimates and Navier-Stokes equations:

  • J.-G. Liu, Jie Liu and R. Pego,
    • Stability and convergence of efficient Navier-Stokes solvers via a commutator estimate
    Comm. Pure App. Math., 60 (2007) 1443--1487. PDF file

  • J.-G. Liu and R. Pego,
    • Stable discretization of magnetohydrodynamics in bounded domains
    to appear in Commun. Math. Sci. PDF file

  • J.-G. Liu, J. Liu and R. Pego,
    • Error estimates for finite-element Navier-Stokes solvers without standard inf-sup conditions
    to appear in Chin. Ann. Math. PDF file

  • J.-G. Liu and W.-C. Wang,
    • Characterization and regularity for axisymmetric solenoidal vector fields with application to Navier-Stokes equation
    to appear in SIAM J. Math. Anal. PDF file

  • J.-G. Liu, Jie Liu and R. Pego,
    • On incompressible Navier-Stokes dynamics: a new approach for analysis and computation
    in "Proceedings of the Tenth International Conference on Hyperbolic Problems",
    edited by F. Asakura, etc, Yokohama Publishers, Inc. (2006) 29--44. PDF file

  • J.-G. Liu, Jie Liu and R. Pego,
    • Estimates on the Stokes pressure by partitioning the energy of harmonic functions ,
    in "Kyoto Conference on the Navier-Stokes equations and their Applications",
    edited by Y. Giga, H. Kozono, H. Okamoto and Y. Shibta, RIMS Kokyuroku Bessatsu B1, Kyoto Univ. (2007) 251--270. PDF file

  • H. Johnston and J.-G. Liu,
    • Accurate, stable and efficient Navier-Stokes solvers based on explicit treatment of the pressure term
    J. Comput. Phys. 188 (2004) 221-259. PDF file

  • H. Johnston and J.-G. Liu,
    • Finite difference schemes for incompressible flow based on local pressure boundary condition
    J. Comput. Phys. 180 (2002), 120--154. PDF file

    Flocking and swarming dynamics:

  • S.-Y. Ha and J.-G. Liu
    • A simple proof of the Cucker-Smale flocking dynamics and mean-field limit
    Commun. Math. Sci. 7 (2009), 297 - 325 PDF file

    Multiscale modeling & simulation:

  • P. Degond, J.-G. Liu and L. Mieussens,
    • Macroscopic fluid modes with localized kinetic upscaling effects
    Multiscale Model. Simul. 5 (2006) 695--1043 PDF file

  • P. Degond, S. Jin and J.-G. Liu,
    • Mach-number uniform asymptotic-preserving Gauge schemes for compressible flows
    Bulletin of the Institute of Mathematics Academia Sinica (New Series) 2 (2007), no. 4, 851--892. PDF file

  • P. Degond, J.-G. Liu and M-H Vignal,
    • Analysis of an asymptotic preserving scheme for the Euler-Poisson system in the quasineutral limit
    SIAM J. Num. Anal., 46 (2008), 1298--1322 PDF file

  • B. Engquist and J.-G. Liu,
    • Numerical methods for oscillatory solutions to hyperbolic problems
    Comm. Pure Appl. Math. 46 (1993), 1327--1361. PDF file

    Consistence numerical dissipation in solid mechanics:

  • S. Antman and J.-G. Liu
    • Basic themes and pretty problems of nonlinear solid mechanics
    Milan J. Math, 75 (2007) 135--176. PDF file

    Coarsening dynamics in thin film epitaxy:

  • W. Bao and J.-G. Liu (editors)
    • Dynamics in Models of Coarsening, Coagulation, Condensation and Quantization ,
    World Scientific, 2007, SBN-10: 9812708502, ISBN-13: 9789812708502.

  • B. Li and J.-G. Liu,
    • Eptaxial growth without slope selection: energetics, coarsening, and dynamic scaling
    J. Nonlinear Sci., 14 (2004) 429-451. PDF file

  • B. Li and J.-G. Liu,
    • Thin film epitaxy with or without slope selection
    European J. Applied Math., 14 , (2003) 713-743. PDF file

    Electrostatics for bio-molecules in solution:

  • I.-L. Chern, J.-G. Liu and W.-C. Wang,
    • Accurate Evaluation of Electrostatics for Macromolecules in Solution ,
    Methods and Applications of Analysis, 10 (2003) 309-328. PDF file

    Vortex sheets and Kelvin-Helmholtz instability:

  • J.-G. Liu and Z. Xin,
    • Convergence of point vortex method for 2-D vortex sheet
    Math. Comp. 70 (2001) 565-606. PDF file

  • J.-G. Liu and Z. Xin,
    • Convergence of vortex methods for weak solutions to the 2-D Euler equations with vortex sheets data
    Comm. Pure Appl. Math. 48 (1995), 611-628. PDF file

    Boundary layer separation and wake flow:

  • Y.-L. Huang, J.-G. Liu and W.-C. Wang
    • An FFT based fast Poisson solver on spherical shells
    to appear in Commun. Comput. Phy. PDF file

  • M. Ghil, J.-G. Liu, C. Wang and S. Wang,
    • Boundary-layer separation and adverse pressure gradient for 2-D viscous incompressible flow
    Physica D, 197 (2004) 149--173. PDF file

  • Z.J. Wang, S. Childress and J.-G. Liu,
    • Connection between corner vortices and shear layer instability in flow past an ellipse
    Phys. Fluids. 11 (1999) 2446-2448. PDF file

    Kinetic boundary layer:

  • J.-G. Liu and Z. Xin,
    • Boundary layer behavior in the fluid-dynamic limit for a nonlinear model Boltzmann equation
    Arch. Rat. Mech. Anal. 135 (1996) 61--105. PDF file
    Received a Featured Review from Math. Rev.

  • J.-G. Liu and Z. Xin,
    • Kinetic and viscous boundary layers for the Broadwell equations
    Transport Theory Statist. Phys. 25 (1996) 447--461.

    Dispersive scheme and dispersive wave:

  • C.D. Levermore and J.-G. Liu,
    • Large oscillations arising from a dispersive numerical scheme
    Physica D, 99 (1996) 191-216. PDF file

  • S. Jin and J.-G. Liu,
    • Relaxation and diffusion enhanced dispersive waves
    Proc. Roy. Soc. Lon. A 446 (1994) 555-563.

    Nonlinear stability of shock profile:

  • J.-G. Liu and Z. Xin,
    • Nonlinear stability of discrete shocks for systems of conservation laws
    Arch. Rat. Mech. Anal. 125 (1993), 217--256. PDF file

  • J.-G. Liu and Z. Xin,
    • L1-stability of stationary discrete shocks
    Math. Comp. 60 (1993), 233--244. PDF file

    Energy and helicity preserving schemes:

  • J.-G. Liu and W.C. Wang,
    • Convergence analysis of the energy and helicity preserving scheme for axisymmetric flows
    SIAM J Numer. Anal. 44 (2006) 2456-2480. PDF file

  • J.-G. Liu and W.C. Wang,
    • Energy and helicity preserving schemes for hydro- and magnetohydro-dynamics flows with symmetry
    J. Comput. Phys., 200 (2004) 8-33. PDF file

  • J.-G. Liu and W.C. Wang,
    • An energy preserving MAC-Yee scheme for the incompressible MHD equation
    J. Comput. Phys. 174 (2001), 12--37. PDF file

    Numerical methods for geophysical flow:

  • J.-G. Liu and C. Wang,
    • A fourth order numerical method for the primitive equations formulated in mean vorticity
    Commun. Comput. Phys. 4 (2008), 26 - 55 PDF file

  • J.-G. Liu, R. Samelson and C. Wang,
    • Global weak solution of planetary geostrophic equations with inviscid geostrophic balance
    Applicable Analysis, 85 (2006), 593 - 605 PDF file

    Gauge methods and projection methods for incompressible flow:

  • Weinan E and J.-G. Liu,
    • Gauge method for viscous incompressible flows
    Comm. Math. Sci., 1 (2003), 317--332. PDF file

  • Weinan E and J.-G. Liu,
    • Gauge finite element method for incompressible flows
    Int. J. Num. Meth. Fluids, 34 (2000) 701-710. PDF file

  • C. Wang and J.-G. Liu,
    • Convergence of gauge method for incompressible flow
    Math. Comp. 69 (2000), 1385-1407. PDF file

  • Weinan E and J.-G. Liu,
    • Finite difference schemes for incompressible flows in the impulse-velocity formulation
    J. Comput. Phys. 130 (1997) 67-76. PDF file

  • Weinan E and J.-G. Liu,
    • Projection method I: convergence and numerical boundary layers,
    SIAM J. Numer. Anal., 32 (1995) 1017-1057. PDF file

  • Weinan E and J.-G. Liu,
    • Projection method II: Godunov-Ryabenki analysis
    SIAM J. Numer. Anal., 33 (1996) 1597--1621. PDF file

  • Weinan E and J.-G. Liu,
    • Projection method III: spatial discretization on the staggered grid
    Math. Comp. 71 (2002), 27--47. PDF file

  • P. Lin, J.-G. Liu and X. Lu,
    • Long time numerical solutyion of the Navier-Stokes equations based on a sequential regularization formulation
    SIAM J. Sci. Comput. 31 (2008), 398--419 PDF file

  • X. Lu, P. Lin and J.-G. Liu,
    • Analysis of a sequential regularization method for the unsteady Navier-Stokes equations
    Math. Comp., 77 (2008) 1467--1494. PDF file

    Vorticity based numerical methods:

  • J.-G. Liu and Weinan E
    • Simple finite element method in vorticity formulation for incompressible flow
    Math. Comp. 69 (2001) 1385-1407. PDF file

  • J.-G. Liu and C. Wang
    • High order finite difference method for unsteady incompressible flow on multi-connected domain in vorticity-stream function formulation
    Computer and Fluids, 33 (2004) 223-255. PDF file

  • C. Wang and J.-G. Liu,
    • Analysis of finite difference schemes for unsteady Navier-Stokes equations in vorticity formulation
    Numer. Math. 91 (2002), 543--576. PDF file

  • C. Wang and J.-G. Liu,
    • Fourth order convergence of a compact difference solver for incompressible flow
    Commun. Appl. Anal. 7 , (2003), 171-191.

  • Weinan E and J.-G. Liu,
    • Essential compact scheme for unsteady viscous incompressible flows,
    J. Comput. Phys. 126 (1996) 122--138. PDF file

  • Weinan E and J.-G. Liu,
    • Vorticity boundary condition and related issues for finite difference schemes
    J. Comput. Phys. 124 (1996) 368--382. PDF file

  • Weinan E and J.-G. Liu,
    • Finite difference methods for 3D viscous incompressible flows in the vorticity-vector potential formulation on non-staggered grids
    J. Comput. Phys. 138 (1997) 57--82. PDF file

    Numerical methods for Boussinesq equations:

  • J.-G. Liu, C. Wang and H. Johnston,
    • A fourth order compact scheme for incompressible Boussinesq equations
    J. Sci. Comput. 18 (2003) 253-285. PDF file

  • C. Wang, J.-G. Liu and H. Johnston,
    • Analysis of a fourth order finite difference method for the incompressible Boussinesq equations
    Numer. Math., 97 (2004) 555--594. PDF file

    Discontinuous Galerkin method for incompressible flow:

  • J.-G. Liu and C.-W. Shu,
    • A high order discontinuous Galerkin method for incompressible flows
    J. Comput. Phys. 160 (2000) 577-596. PDF file

  • J.-G. Liu and Z. Xin,
    • Convergence of a Galerkin method for 2-D discontinuous Euler flows
    Comm. Pure Appl. Math. 53 (2000) 786-798. PDF file

    Shock capturing schemes:

  • K. Duraisamy, J.D. Baeder and J.-G. Liu,
    • Concepts and application of time limiters to high resolution schemes
    J. Sci. Comput. 19 (2003) 139-162. PDF file

  • C. Wang and J.-G. Liu,
    • Positivity property of second-order flux-splitting schemes for the compressible Euler equations
    Discrete Contin. Dyn. Syst. Ser. B 3 (2003) 201-228. PDF file

  • H. Choi and J.-G. Liu,
    • The reconstruction of upwind fluxes for conservation laws, its behavior in dynamic and steady state calculations
    J. Comput. Phys. 144 (1998) 237--256. PDF file

  • S. Jin and J.-G. Liu,
    • The effects of numerical viscosities I: slowly moving shocks
    J. Comput. Phys. 126 (1996) 373-389. PDF file

  • S. Jin and J.-G. Liu,
    • Oscillations induced by numerical viscosities,
    Mat. Contemp. 10 (1996) 169-180. PDF file

    Entropy conditions in shock capturing schemes:

  • P. Lefloch and J.-G. Liu,
    • Generalized monotone schemes, discrete paths of extrema, and discrete entropy conditions
    Math. Comp. 68 (1999) 1025-1055. PDF file

  • G.-Q. Chen and J.-G. Liu,
    • Convergence of difference schemes with high resolutions to conservation laws
    Math. Comp. 66 (1997) 1027--1053. PDF file

  • P. Lefloch and J.-G. Liu,
    • Discrete entropy and monotonicity criteria for hyperbolic conservation laws
    C.R. Acad. Sci. Paris. 319 (1994), 881--886.

  • G.-Q. Chen and J.-G. Liu,
    • Convergence of second-order schemes for isentropic gas dynamics
    Math. Comp. 61 (1993), 607--629. PDF file

    Drift-diffusion equations for semiconductor :

  • C. Chainais-Hillairet, J.-G. Liu and Y.-J. Peng,
    • Finite volume scheme for multi-dimensional drift-diffusion equations and convergence analysis
    Math. Model. Numer. Anal., 37 (2003) 319-338. PDF file

    Far field boundary conditions and effects of small viscosity:

  • J.-G. Liu, and W.-Q. Xu,
    • Far field boundary condition for convection diffusion equation at zero viscosity limit
    Q APPL MATH vol 62 (2004) 27-52. PDF file

  • H.-E. Lin, J.-G. Liu, and W.-Q. Xu,
    • Effects of small viscosity and far field boundary conditions for hyperbolic systems
    Communications on Pure and Applied Analysis, vol 3 (2004) 267-290. PDF file

    Mathematical Finance and Applied Statistics:

  • E. Xu and J.-G. Liu,
    • Pricing of mortgage-backed securities with option-adjusted spread
    Managerial Finance, 24 (1998) 94-109. PDF file

  • J. Moore, J.-G. Liu, K. Zhou, S. Haley, and L. Yu,
    • Effects of genotype and environment on the antioxidant properties of hard winter wheat bran
    J Agric Food Chem, (2006), 54, 5313-5322. PDF file

  • J. Moore, Z. Cheng, J. Hao, G. Guo, J.-G. Liu, C. Lin and L. Yu,
    • Effects of solid-state yeast treatment on the antioxidant properties and protein and fiber compositions of common hard wheat bran
    J Agric Food Chem, (2007), 55, 10173--10182. PDF file