**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, Vol. 8, issue 1 (March 2010), p.1-25. See the whole special issue.**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**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.**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, accepted March 2011.**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**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.**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.**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.**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.**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 .**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.**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**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.**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**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.)**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

**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.**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.**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**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**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**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**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.***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**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**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**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.**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.**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**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.**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**A second order in time, decoupled, unconditionally stable numerical scheme for the Cahn-Hilliard-Darcy system**, with Daozhi Han. Submitted Aug. 2016.

**Nonlinear Dynamics and Statistical Theories for Basic Geophysical Flows**

with Andrew J. Majda

*Cambridge University Press*, 2006.