Selected Publications

  • A Remark on the Characterization of the Gradient of Distributions
    Applicable Analysis, vol 51, 1993, 35-40.
  • An Energy Equation for Weakly Damped Driven Nonlinear Schrödinger Equations and Its Application to Their Attractors
    Physica D, 88 (1995) 167-175.
  • Upper Bound on the Dimension of the Attractor for the Nonhomogeneous Navier-Stokes Equations
    With Alain Miranville
    Discrete and Continuous Dynamical Systems, Vol 2, No. 1, 1996, pp. 95-110.
  • Time Averaged Energy Dissipation Rate of Boundary Driven Flows
    Physica D, 99 (1997) 555-563
  • Asymptotic Analysis of Oseen Type Equations in a Channel at High Reynolds Number
    With Roger Temam
    Indiana Univ. Math. J., 45(3), 1996, pp. 863-916.
  • Attractor Dimension Estimates for Two-dimensional Shear Flows
    With Charles Doering
    Physica D, 123 (1998) 206-222.
  • Attractors for Non-Compact Semigroups via Energy Equations
    with Ioana Moise and Ricardo Rosa
    Nonlinearity, 11, 1998, 1369-1393.
  • Selective Decay for Geophysical Flows
    with Andrew Majda and Sang-Yeun Shim, Dedicated to Cathleen Morawetz on the occasion of her 75th birthday,
    Methods and Applications of Analysis, vol. 7, no. 3, pp. 511 - 554, 2000.
  • Effect of tangential derivatives in the boundary layer on the energy dissipation rate
    Physica D, 144(2000) 142-153.
  • Remarks on the Prandtl type equations with permeable wall
    with Roger Temam
    Zeitschrift fur Angewandte Mathematik und Mechanik (ZAMM), 80 (2000), 11-12, 835-843.
  • A Kato type theorem on zero viscosity limit of Navier-Stokes flows
    Indiana Univ. Math. Jour., 50, No.1 (2001), 223-241.
  • Boundary Layer Associated with the Incompressible Navier-Stokes Equations: the non-characteristic boundary case
    with Roger Temam
    J. Diff. Eqs., 179, (2002), 647-686.
  • Infinite Prandtl number limit of Rayleigh-Benard convection
    CPAM, 57, (2004) no.10, p.1265-1282.
  • A Note on Long Time Behavior of Solutions to the Boussinesq System at Large Prandtl Number
    Contemporary Mathematics, 371, (2005), pp. 315-323.
  • The validity of the one and one-half layer model and effective topography
    with Andrew Majda
    Comm. PDE, Volume 30, Number 9, 2005, pp. 1305 - 1314
  • The emergence of large scale coherent structure under small scale random bombardments
    with Andrew Majda
    CPAM, Volume 59, Issue 4 (2006), pp.467-500.
  • Asymptotic Behavior of the Global Attractors to the Boussinesq System for Rayleigh-Bénard Convection at Large Prandtl Number
    CPAM, vol, 60, issue 9, pp.1293-1318, 2007.
  • A Discrete Kato Type Theorem on Inviscid Limit of Navier-Stokes Flows
    with Wendy Cheng,
    J. Math. Phys., vol.48, issue6, 065303 (2007).
  • Stationary statistical properties of Rayleigh-Bénard convection at large Prandtl number
    CPAM, 61 (2008), no. 6, 789--815, DOI:10.1002/cpa.20214.
  • Bound on vertical heat transport at large Prandtl number
    Physica D, 237 (2008), 854-858, DOI:10.1016/j.physd.2007.11.001.
  • Upper semi-continuity of stationary statistical properties of dissipative systems
    Discrete and Continuous Dynamical Systems, A (an invited article to the special issue dedicated to Prof. Li Ta-Tsien) Vol. 23, no.1/2, pp.521-540, 2009. doi:10.3934/dcds.2009.23.521
  • A semi-implicit scheme for stationary statistical properties of the infinite Prandtl number model,
    with Wendy Cheng
    SIAM Jour. Num. Anal. vol.47, no.1, 250-270, 2008. DOI.10.1137/080713501
  • Coupled Stokes-Darcy Model with Beavers-Joseph Interface Boundary Condition,
    with Yanzhao Cao, Max Gunzburger and Fei (Neil) Hua,
    Comm. Math. Sci., an invited article in the special issue dedicated to Andy Majda, accepted July 2008.
  • Approximation of stationary statistical properties of dissipative dynamical systems: time discretization.
    Math. Comp., available online April 20, 2009. DOI: 10.1090/S0025-5718-09-02256-X
  • Linear response theory for statistical ensembles in complex systems with time-periodic forcing.
    with Andrew Majda
    Comm. Math. Sci., an invited article in the special issue dedicated to Andy Majda, submitted Sept. 2008, accepted Dec. 2008.
  • Well-posedness of the infinite Prandtl number model for convection with temperature-dependent viscosity,
    with Max Gunzburger and Yuki Saka,
    Analysis and Applications, Vol. 7, No. 3 (2009) 297-308.
  • A parallel Robin-Robin domain decomposition method for the Stokes-Darcy system ,
    with Wenbin Chen, Max Gunzburger and Fei (Neil) Hua. Submitted Sept. 2008. SINUM#074055
  • Unconditionally stable schemes of equations for thin film epitaxy ,
    with Cheng Wang and Steven Wise, DCDS-A, accepted Nov. 2009 (an invited article in the special issue dedicated to Roger Temam).
  • On the coupled continuum pipe flow model (CCPF) for flows in karst aquifer
    DCDS-B, accepted Oct. 2009.
  • Boundary layer associated with the Darcy-Brinkman-Boussinesq model for convection in porous media,
    with James Kelliher and Roger Temam, submitted Nov. 2009.
  • Nonlinear Dynamics and Statistical Theories for Basic Geophysical Flows
    with Andrew J. Majda
    Cambridge University Press , 2006.
    • Research supported in part by grants from the National Science Foundation