Selected Publications

  1. A Remark on the Characterization of the Gradient of Distributions
    Applicable Analysis, vol 51, 1993, 35-40.
  2. An Energy Equation for Weakly Damped Driven Nonlinear Schrödinger Equations and Its Application to Their Attractors
    Physica D, 88 (1995) 167-175.
  3. 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.
  4. Time Averaged Energy Dissipation Rate of Boundary Driven Flows
    Physica D, 99 (1997) 555-563
  5. 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.
  6. Attractor Dimension Estimates for Two-dimensional Shear Flows
    With Charles Doering
    Physica D, 123 (1998) 206-222.
  7. Attractors for Non-Compact Semigroups via Energy Equations
    with Ioana Moise and Ricardo Rosa
    Nonlinearity, 11, 1998, 1369-1393.
  8. 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.
  9. Effect of tangential derivatives in the boundary layer on the energy dissipation rate
    Physica D, 144(2000) 142-153.
  10. 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.
  11. A Kato type theorem on zero viscosity limit of Navier-Stokes flows
    Indiana Univ. Math. Jour., 50, No.1 (2001), 223-241.
  12. Boundary Layer Associated with the Incompressible Navier-Stokes Equations: the non-characteristic boundary case
    with Roger Temam
    J. Diff. Eqs., 179, (2002), 647-686.
  13. Infinite Prandtl number limit of Rayleigh-Benard convection
    CPAM, 57, (2004) no.10, p.1265-1282.
  14. A Note on Long Time Behavior of Solutions to the Boussinesq System at Large Prandtl Number
    Contemporary Mathematics, 371, (2005), pp. 315-323.
  15. 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
  16. The emergence of large scale coherent structure under small scale random bombardments
    with Andrew Majda
    CPAM, Volume 59, Issue 4 (2006), pp.467-500.
  17. 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.
  18. A Discrete Kato Type Theorem on Inviscid Limit of Navier-Stokes Flows
    with Wendy Cheng,
    J. Math. Phys., vol.48, issue6, 065303 (2007).
  19. Stationary statistical properties of Rayleigh-Bénard convection at large Prandtl number
    CPAM, 61 (2008), no. 6, 789--815, DOI:10.1002/cpa.20214.
  20. Bound on vertical heat transport at large Prandtl number
    Physica D, 237 (2008), 854-858, DOI:10.1016/j.physd.2007.11.001.
  21. 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
  22. 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
  23. 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, Vol. 8, issue 1 (March 2010), p.1-25. See the whole special issue.
  24. Approximation of stationary statistical properties of dissipative dynamical systems: time discretization.
    Math. Comp., available online April 20, 2009, vol. 79 (2010) 259-280. DOI: 10.1090/S0025-5718-09-02256-X
  25. 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, Vol. 8, issue 1 (March 2010), p.145-172. See the whole special issue.
  26. 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.
  27. 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, accepted March 2011.
  28. 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). pp. 405-423, DCDS-A vol. 28 issue 1 September 2010. doi:10.3934/dcds.2010.28.405
  29. On the coupled continuum pipe flow model (CCPF) for flows in karst aquifer
    DCDS-B, accepted Oct. 2009. Volume: 13, Number: 2, March 2010, p. 489-501.
  30. Boundary layer associated with the Darcy-Brinkman-Boussinesq model for convection in porous media, revised version,
    with James Kelliher and Roger Temam, accepted to PHYSICA D, Dec. 2010. Published online at http://dx.doi.org/10.1016/j.physd.2010.11.012.
  31. Examples of boundary layer associated with the incompressible Navier-Stokes equations ,
    Chinese Annals of Mathematics, ser. B,vol. 31, no.5, pp.781-792, 2010 special issue dedicated to Prof. Temam.
  32. Boundary layer associated with a class of 3D nonlinear plane parallel channel flows ,
    with Anna Mazzucato and Dongjuan Niu, Aug. 2010, accepted to IUMJ March 2011. #4479, vol. 60, no.4, 2011, pp. 1113-1136.
  33. Approximation of the stationary statistical properties of the dynamical systems generated by the two-dimensional Rayleigh-Benard convection problem ,
    with Florentina Tone, Analysis and Applications, vol. 09, no. 4, (2011) 421-446. DOI: 10.1142/S0219530511001935 .
  34. Well-posedness of the Hele-Shaw-Cahn-Hilliard system
    with Zhifei Zhang, submitted Aug. 2010, under minor revision, ANIHPC-D-10-00071, accepted June 2012. DOI:10.1016/j.anipc.2012.06.003 \item {\it Well-posedness of the Hele-Shaw-Cahn-Hilliard system}, Xiaoming Wang and Zhifei Zhang*, submitted to {\sc Annales de l'Institut Henri PoincarC) (C) Analyse Non LinC)aire.}, Dec. 2010. accepted June 2012. DOI:10.1016/j.anipc.2012.06.003, Volume 30, Issue 3, May-June 2013, pp. 367-384.
  35. A linear energy stable numerical scheme for epitaxial thin film growth model without slope selection
    with Wenbin Chen, Sidafa Conde, Cheng Wang and Steven Wise, submitted to J. Sci. Comp. Dec. 2010, accepted Nov. 2011 (JOMP693R1)., (2012) 52: 546-562 DOI: 10.1007/s10915-011-9559-2
  36. Long-time Behavior for the Hele-Shaw-Cahn-Hilliard System
    with Hao Wu, submitted to Asymptotic Analysis in Jan. 2011, accepted Sept. 2011. (manuscript#: AA1681), vol. 78, no.1, Aug. 2012, pp.217-245.
  37. Second-order convex splitting schemes for gradient flows with Enhrich-Schwoebel type energy: application to thin film epitaxy
    with Jie Shen, Cheng Wang and Steven Wise, submitted to SINUM, Jan. 2011, accepted Nov. 2011. SIAM J. Numer. Anal. vol. 50, no.1, pp.105-125. http://dx.doi.org/10.1137/110822839
  38. Calibrating the exchange coefficient in the modified coupled continuum pipe-flow model for flow in karst aquifers
    with Nan Chen, Max Gunzburger, Bill Hu and Celestine Woodruff, submitted to J. Hydrology, Mar. 2011, accepted Nov. 2011. DOI: 10.1016/j.jhydrol.2011.11.001 (This is my first paper without a theorem. I still retain the alphabetic order of the authors though.)
  39. Long time stability of a classical efficient scheme for two dimensional Navier--Stokes equations
    with Sigal Gottlieb, Florentina Tone, Cheng Wang and Djoko Wirosoetisno, submitted to SINUM May 2011, accepted Nov. 2011, http://arxiv.org/abs/1105.4349. SIAM J. Numer. Anal. 50, pp. 126-150. http://dx.doi.org/10.1137/110834901
  40. An efficient second order in time scheme for approximating long time statistical properties of the two dimensional Navier-Stokes equations submitted to Numer. Math., Sept. 2011, http://arxiv.org/abs/1108.5409, under minor revision, Jan. 2012, accepted Feb. 2012, Volume 121, Issue 4 (2012), Page 753-779. DOI: 10.1007/s00211-012-0450-3.
  41. Boundary layer for a class of nonlinear pipe flow with Daozhi Han, Anna Mazzucato and Dongjuan Niu, submitted Nov. 2011 to JDE, http://arxiv.org/abs/????. Under minor revision, Jan. 2012, accepted Feb. 2012,YJDEQ6807, Volume 252, Issue 12, 15 June 2012, Pages 6387-6413, DOI:10.1016/j.jde.2012.02.012.
  42. A bound on the vertical transport of heat in the ultimate state of slippery convection at large Prandtl numbers , with Jared Whitehead, submitted to JFM, May 2012, accepted May 2013. Volume 729 / August 2013, pp 103-122, DOI: http://dx.doi.org/10.1017/jfm.2013.289 (About DOI), Published online: 17 July 2013
  43. Efficient and long time accurate second-order methods for Stokes-Darcy system, with Wenbin Chen, Max Gunzburger and Dong Sun, submitted to SINUM, December 2012, accepted June 2013. SIAM J. Numer. Anal. 51-5 (2013), pp. 2563-2584 http://dx.doi.org/10.1137/120897705
  44. Initial Boundary Layer Associated with the Nonlinear Darcy-Brinkman System, with Daozhi Han (submitted June 2013, accepted September 2013). J. Differential Equations, vol. 256, 2014, pp. 609-639. DOI:10.1016/j.jde.2013.09.014
  45. Two phase flows in karstic geometry, with Daozhi Han and Dong Sun, submitted to MMAS August 2013, accepted November 2013. Vol. 37, no.18, pages 3048-3063, Nov. 2014. DOI: 10.1002/mma.3043
  46. Existence and uniqueness of global weak solutions to a Cahn-Hilliard-Stokes-Darcy system for two phase incompressible flows in karstic geometry, with Daozhi Han and Hao Wu (submitted May 2014, accepted July 2014). , Volume 257, Issue 10, 15 November 2014, Pages 3887. DOI: 10.1016/j.jde.2014.07.013, available online at http://authors.elsevier.com/sd/article/S0022039614003167.
  47. Long-time dynamics of 2d double-diffusive convection: analysis and/of numerics with Florentina Tone and Djoko Wirosoetisno (accepted Oct. 2014). Numerische Mathematik July 2015, Volume 130, Issue 3, pp 541-566. DOI: 10.1007/s00211-014-0670-9
  48. A second order in time, uniquely solvable, unconditionally stable numerical scheme for Cahn-Hilliard-Navier-Stokes equation , with Daozhi Han (submitted to July 2014, accepted February 2015). Journal of Computational Physics (2015), pp. 139-156 DOI: 10.1016/j.jcp.2015.02.046
  49. An efficient and long-time accurate third-order algorithm for the Stokes-Darcy system, with Wenbin Chen, Max Gunzburger and Dong Sun. Submitted to Numer. Math. in April 2015, accepted November 2015, published online December, 2015, (2016) 134(4), 857-879, DOI: 10.1007/s00211-015-0789-3
  50. Numerical algorithms for stationary statistical properties of dissipative dynamical systems, an invited paper dedicated to Prof. Peter Lax on the occasion of his 90th birthday. Accepted Feb. 2016. DCDS-A, vol. 36 no.8, pp. 4599-4618, August 2016.
  51. Decoupled energy-law preserving numerical schemes for the Cahn-Hilliard-Darcy system, with Daozhi Han. Submitted to NMPDE June 2015, accepted Nov. 2015. vol. 32, no.3, May 2016, pp. 936--954.
  52. Initial boundary layer associated with the nonlinear Darcy-Brinkman-Oberbeck-Boussinesq system, with Mingwen Fei and Daozhi Han. Submitted to Physica D Feb. 2016, published online Aug. 2016. http://dx.doi.org/10.1016/j.physd.2016.08.002
  53. Convergence Analysis and Error Estimates for a Second Order Accurate Finite Element Method for the Cahn-Hilliard-Navier-Stokes System, with Amanda E. Diegel, Cheng Wang, and Steven M. Wise. Submitted to Numer. Math. June 2016, accepted March 2017.
  54. Uniquely solvable and energy stable decoupled schemes for Cahn-Hilliard-Stokes-Darcy system for two-phase flows in karstic geometry, with Wenbin Chen and Daozhi Han. Submitted to Numer. Math. Aug. 2016, under revision, Nov. 2016, accepted Jan. 2017. DOI: 10.1007/s00211-017-0870-1
  55. A second order in time, decoupled, unconditionally stable numerical scheme for the Cahn-Hilliard-Darcy system, with Daozhi Han. Submitted Aug. 2016.
  56. Nonlinear Dynamics and Statistical Theories for Basic Geophysical Flows
    with Andrew J. Majda
    Cambridge University Press , 2006.
I also work on sinkhole formation and collapse.
  • Some of our lab experiments on sinkhole formation and collapse have been filmed (using gopro) and posted on Youtube by a student.
  • A short video produced by FSU on the project can be found on Youtube
  • Our work is also featured in a recent NPR/WFSU news clip.
  • The same lab experiments are featured in a new PBS NOVA program: Sinkholes - Buried alive which was first aired on Wednesday, January 28th, 2015.
    • Research supported in part by grants from the National Science Foundation and the Florida State University.