Teaching The only good is knowledge and the only evil is ignorance.  Socrates
Previous semesters
Old Webwork is on http://sibilant.math.ttu.edu Spring 2020. MATH3350021. Higher Mathematics for Engineers and Scientists I.
 Spring 2020. MATH3350022. Higher Mathematics for Engineers and Scientists I.
 Fall 2019 MATH4351001. Advanced Calculus II.
 Fall 2019 MATH2450022. Calculus III With Applications.
 Spring 2019. MATH5332001. Partial Differential Equations I. (Ph.D. Prelim.)
 Spring 2019. MATH4354002. Differential equations II.
 Fall 2018. MATH3354002. Differential equations I.
 Fall 2018. MATH3351002. Higher Mathematics for Engineers and Scientists II.
 Spring 2018. MATH3354001. Differential equations I.
 Spring 2018. MATH4354002. Differential equations II.
 Spring 2017. MATH3350013. Higher Mathematics for Engineers and Scientists I.
 Spring 2017. MATH3351001. Higher Mathematics for Engineers and Scientists II.
 Summer II, 2016. MATH3350202. Higher Mathematics for Engineers and Scientists I.
 Spring 2016. MATH5332001. Partial Differential Equations I. (Ph.D. Prelim.)
 Spring 2016. MATH3351002. Higher Mathematics for Engineers and Scientists II.
 Fall 2015. MATH3351004. Higher Mathematics for Engineers and Scientists II.
 Fall 2015. MATH3350016. Higher Mathematics for Engineers and Scientists I.
 Spring 2015. MATH5332001. Partial Differential Equations I. (Ph.D. Prelim.)
 Spring 2015. MATH4351001. Advanced Calculus II. (undergraduate math majors)
 Fall 2014. MATH4350002. Advanced Calculus I. (undergraduate math majors)
 Fall 2014. MATH1320030. College Algebra.
 Spring 2014. MATH3310002. Introduction to Mathematical Reasoning and Proof.
 Spring 2014. MATH2360008. Linear Algebra.
 Fall 2013. MATH1451H01. Calculus I With ApplicationsHonors.
 Fall 2013. MATH2360001. Linear Algebra.
 Spring 2013. MATH5099011. Partial Differential Equations III. (graduate level)
 Spring 2013. MATH4354001. Differential Equations II.
 Fall 2012. MATH5333. Partial Differential Equations II.
 Fall 2012. MATH2450010. Calculus III with Applications.
 Spring 2012. MATH5332. Partial Differential Equations.
 Spring 2012. MATH3351001. Higher Mathematics for Engineers and Scientists II.
 Fall 2011. MATH3350010. Higher Mathematics for Engineers and Scientists I.
 Fall 2011. MATH3350012. Higher Mathematics for Engineers and Scientists I.
 Spring 2011. MATH5341001. Functional Analysis II.
 Spring 2011. MATH5332001. Partial Differential Equations.
 Fall 2010. MATH5340001. Functional Analysis.
 Fall 2010. MATH2360002. Linear Algebra.
 Spring 2010. MATH4354001. Differential Equations II.
 Spring 2010. MATH1352026. Calculus II.
 Fall 2009. MATH3354002. Differential Equations I.
 Fall 2009. MATH1351026. Calculus I.
 Spring 2009. MATH3350010. Higher Mathematics for Engineers and Scientists I.
 Fall 2008. MATH3350008. Higher Mathematics for Engineers and Scientists I.
Research What we know is a drop, what we don't know is an ocean.  Isaac Newton
Research interest
 Partial differential equations
 Fluid dynamics
 Porous medium equations
 Dynamical systems
Publications
(All papers are in peer reviewed journals. List in PDF.) Asymptotic expansions with exponential, power, and logarithmic functions for nonautonomous nonlinear differential equations, (with Dat Cao,) 144, submitted. [Preprint]
 Slightly compressible Forchheimer flows in rotating porous media. I., (with Emine Celik, Thinh Kieu,) 148, submitted. [Preprint]
 Asymptotic expansions for the Lagrangian trajectories from solutions of the NavierStokes equations, Communications in Mathematical Physics, 116, accepted. [Preprint]
 Asymptotic expansions in time for rotating incompressible viscous fluids, (with Edriss Titi,) Annales de l'Institut Henri Poincare  Analyse non lineaire, 129, in press. (doi:10.1016/j.anihpc.2020.06.005)
 Asymptotic expansions in a genral system of decaying functions for the NavierStokes equations, (with Dat Cao,) Annali di Matematica Pura ed Applicata, Vol. 199, No. 3 (June 2020), 10231072. (doi:10.1007/s10231019009113)
 Longtime asymptotic expansions for NavierStokes equations with powerdecaying forces, (with Dat Cao,) Proceedings of the Royal Society of Edinburgh: Section A Mathematics, Vol. 150, No.2 (April 2020), 569606. (doi:10.1017/prm.2018.154)
 Global estimates for generalized Forchheimer flows of slightly compressible fluids, (with Thinh Kieu,) Journal d'Analyse Mathematique, March 2019, Volume 137, Issue 1, 155. (doi:10.1007/s1185401800645) SharedIt
 Doubly nonlinear parabolic equations for a general class of Forchheimer gas flows in porous media, (with Emine Celik, Thinh Kieu,) Nonlinearity, Vol. 31, No. 8 (2018) 36173650. (doi:10.1088/13616544/aabf05)
 Navier and Stokes meet Poincaré and Dulac, (with Ciprian Foias, JeanClaude Saut,) J. Appl. Anal. Comput., Volume 8, Number 3, June 2018, 727763. (doi:10.11948/2018.727) (survey)
 Asymptotic expansion for solutions of the NavierStokes equations with nonpotential body forces, (with Vicent Martinez,) J. Math. Anal. Appl., Volume 462, Issue 1, (1 June 2018) 84113. (doi:10.1016/j.jmaa.2018.01.065)
 Generalized Forchheimer flows of isentropic gases, (with Emine Celik, Thinh Kieu,) J. Math. Fluid Mech., March 2018, Volume 20, Issue 1, 83115. (doi:10.1007/s0002101603132)
 Continuity of pullback and uniform attractors, (with Eric Olson, James Robinson,) J. Differential Equations, Volume 264, Issue 6, (15 March 2018) 40674093. (doi:10.1016/j.jde.2017.12.002)
 Interior estimates for generalized Forchheimer flows of slightly compressible fluids, (with Thinh Kieu,) Advanced Nonlinear Studies, 17(4), (2017) 739767. (doi:10.1515/ans20166027)
 Asymptotic expansion in Gevrey spaces for solutions of NavierStokes equations, (with Vincent Martinez,) Asymptotic Analysis (2017), vol. 104, no. 34, 167190. (doi:10.3233/ASY171429)
 Fluid flows of mixed regimes in porous media, (with Emine Celik, Akif Ibragimov, Thinh Kieu,) Journal of Mathematical Physics, Volume 58 (2017), No. 2, 023102, 30 pp. (doi:10.1063/1.4976195)
 Maximum estimates for generalized Forchheimer flows in heterogeneous porous media. (with Emine Celik,) J. Differential Equations, Volume 262, Issue 3 (5 February 2017), 21582195. (doi:10.1016/j.jde.2016.10.043)
 Local gradient estimates for degenerate elliptic equations, (with Truyen Nguyen, Tuoc Phan,) Advanced Nonlinear Studies, Volume 16, Issue 3 (Aug 2016), 479489. (doi:10.1515/ans20155038)
 Generalized Forchheimer flows in heterogeneous porous media, (with Emine Celik,) Nonlinearity, Vol. 29, No. 3 (March 2016), 11241155. (doi:10.1088/09517715/29/3/1124)
 Stability of solutions to generalized Forchheimer equations of any degree, (with Akif Ibragimov, Thinh Kieu, Zeev Sobol,) Journal of Mathematical Sciences, Volume 210, Number 4 (2015), 476544. (Also in "Problemy Matematicheskogo Analiza" 81, August 2015, 121178.) (doi:10.1007/s1095801525761)
 On the continuity of global attractors, (with Eric Olson, James Robinson,) Proc. Amer. Math. Soc., Volume 143, Number 10 (2015), 43894395. (doi:10.1090/proc/12598)
 Gradient estimates and global existence of smooth solutions to a crossdiffusion system, (with Truyen Nguyen, Tuoc Phan,) SIAM Journal on Mathematical Analysis, Volume 47, Issue 3 (2015), 21222177. (doi:10.1137/140981447)
 A family of steady twophase generalized Forchheimer flows and their linear stability analysis, (with Akif Ibragimov, Thinh Kieu,) J. Math. Phys. 55, Issue 12 (2014), 123101:32pp. (doi:10.1063/1.4903002)
 Properties of generalized Forchheimer flows in porous media, (with Thinh Kieu, Tuoc Phan,) Problems of Mathematical Analysis, Vol. 76 (August 2014), 133194, and in Journal of Mathematical Sciences, Vol. 202 No. 2, October 2014, 259332. (doi:10.1007/s1095801420452)
 Incompressible fluids in thin domains with Navier friction boundary conditions (II), J. of Math. Fluid Mech., Volume 15, Issue 2, June 2013, 361395. (doi:10.1007/s0002101201230)
 Onedimensional twophase generalized Forchheimer flows of incompressible fluids, (with Akif Ibragimov, Thinh Kieu,) J. Math. Anal. Appl., Volume 401, Issue 2, 15 May 2013, 921938. (doi:10.1016/j.jmaa.2012.12.055)
 Qualitative study of generalized Forchheimer flows with the flux boundary condition, (with Akif Ibragimov,) Adv. Diff. Eq., Volume 17, Numbers 56, May/June 2012, 511556.
 Asymptotic integration of NavierStokes equations with potential forces. II. An explicit PoincaréDulac normal form, (with Ciprian Foias, JeanClaude Saut,) J. Funct. Anal., Vol. 260, Issue 10, (2011) 30073035. (doi:10.1016/j.jfa.2011.02.005)
 Structural stability of generalized Forchheimer equations for compressible fluids in porous media, (with Akif Ibragimov,) Nonlinearity, Volume 24, Number 1 / January 2011, 141. (doi:10.1088/09517715/24/1/001)
 NavierStokes equations with Navier boundary conditions for an oceanic model, (with George Sell,) J. Dyn. Diff. Eqn., Volume 22, Number 3 / September 2010, 563616. (doi:10.1007/s1088401091897)
 Incompressible fluids in thin domains with Navier friction boundary conditions (I), J. of Math. Fluid Mech., Volume 12, Number 3 / August 2010, 435472. (doi:10.1007/s0002100902972)
 Analysis of generalized Forchheimer equations of compressible fluids in porous media, (with Eugenio Aulisa, Lidia Bloshanskaya, Akif Ibragimov,) J. Math. Phys. 50, Issue 10, 103102:44pp (2009). (doi:10.1063/1.3204977)
 The normal form of the NavierStokes equations in suitable normed spaces, (with Ciprian Foias, Eric Olson, Mohammed Ziane,) Annales de l'Institut Henri Poincare  Analyse non lineaire, Volume 26, Issue 5, SeptemberOctober 2009, 16351673. (doi:10.1016/j.anihpc.2008.09.003)
 On the helicity in 3D NavierStokes equations II: The statistical case, (with Ciprian Foias, Basil Nicolaenko,) Comm. Math. Physics, Volume 290, Issue 2 (2009) 679717. (doi:10.1007/s002200090827z)
 A basic inequality for the Stokes operator related to the Navier boundary condition, J. of Diff. Eqn., Volume 245, Issue 9, (1 November 2008) 25852594, (doi:10.1016/j.jde.2008.01.024)
 On the helicity in 3D NavierStokes equations I: The nonstatistical case, (with Ciprian Foias, Basil Nicolaenko,) Proc. London Math. Soc., Volume 94 Number 1 (January 2007) 5390. (doi:10.1112/plms/pdl003)
 On the solutions to the normal form of the NavierStokes equations, (with Ciprian Foias, Eric Olson, Mohammed Ziane,) Indiana Univ. Math. J., Vol. 55, No 2 (2006) 631686. (doi:10.1512/iumj.2006.55.2830)
Work in progress
 On the Lagragian tracjectories for incompressible, viscous fluids. II., in preparation.
 Longtime asymptotic expansions for solutions of differential equations of certain classes, (with Dat Cao, Thinh Kieu,) 20 pages, in preparation.
 Longtime dynamics of fluid flows in geophysical fluid models, (with Animikh Biswas,) 19 pages, in preparation.
 Slightly compressible Forchheimer flows in rotating porous media. II., (with Emine Celik, Thinh Kieu,) 19 pages, in preparation.
 Different types of asymptotic expansions for NavierStokes equations, (with Dat Cao,) in preparation.
 Fluid flows in anisotropic porous media, 12 pages, in preparation.
 NavierStokes equations in unbounded domains, in preparation.
 NavierStokes equations with small vicosity, in preparation.
 Dynamics of statistical solutions for NavierStokes equations, (with Animikh Biswas,) in preparation.
 NavierStokes equations with Navier boundary conditions for thin spherical shells, (with George Sell,) in preparation, 20pp.
 NavierStokes equations with Navier boundary conditions in thin domains: The reduced problem, (with George Sell,) in preparation.
Collaborators
 Past and present collaborators: Eugenio Aulisa, Animikh Biswas, Lidia Bloshanskaya, Dat Cao, Emine Celik, Akif Ibragimov, Thinh Kieu, Vincent Martinez, Truyen Nguyen, Eric Olson, Tuoc Phan, James Robinson, JeanClaude Saut, Edriss Titi, Mohammed Ziane
 In Memoriam: Ciprian Foias (Obituray and tribute), Basil Nicolaenko (2007 Memorial Distinguished Lectures), George R. Sell (2016 dedicated workshop)
Conferences

AMS 2020 Fall Central Sectional Meeting
September 1213, 2020. 
AMS 2019 Fall Eastern Sectional Meeting
Binghamton University, Binghamton, NY, October 1213, 2019.  The 4th Annual Meeting of SIAM Central States Section, Norman, Oklahoma, October 57, 2018.
 2017 Joint Mathematics Meetings, Atlanta, Georgia, January 47, 2017.
 The 11th AIMS Conference on Dynamical Systems,
Differential Equations and Applications
Orlando, Florida, July 1  5, 2016
Coorganizer of special session (SS108) "New Developments in Porous Media" Schedule of talks 
International Conference on Evolution Equations
in conjunction with the 31st annual Shanks Lecture
Vanderbilt University, Nashville, TN, May 1620, 2016 
46th Annual John H. Barrett Memorial Lectures
University of Tennessee, Knoxville, TN, May 1618, 2016  The 40th SIAM Southeastern Atlantic Section Conference (SIAMSEAS). Applied Mathematics.
University of Georgia, Athens, Georgia, March 1213, 2016  2016 Joint Methamatics Meeting
Seattle, Washington, January 6  9, 2016  SIAM Conference on Analysis of Partial Differential Equations
Scottsdale, Arizona, December 710, 2015
Coorganizer of Minisymposium: "Dynamics of Partial Differential Equations" Part I and Part II. Schedule and Abstracts  AMS 2015 Spring Western Sectional Meeting
University of Nevada, Las Vegas, Las Vegas, NV, April 18  19, 2015  The 10th AIMS Conference on Dynamical Systems,
Differential Equations and Applications
Madrid, Spain, July 7  11, 2014  Advances in Mathematical Fluid Mechanics, Stochastic and Deterministic Methods
Lisbon, Portugal, June 30  July 5, 2014  AMS 2014 Spring Central Sectional Meeting
Texas Tech University, Lubbock, TX, April 1113, 2014
Coorganizer of Special Session: NavierStokes Equations and Fluid Dyanmics [Photos]  SIAM conference on Analysis of Partial Differential Equations
Lake Buena Vista, Florida, December 710, 2013
Coorganizer of MiniSymposium: Elliptic and Parabolic Equations with Nonstandard Nonlinearity. Speakers and Talks
Invited talk in MiniSymposium: Global Attractors, Dissipative Dynamical Systems, and Turbulence  SIAM conference on Mathematical and Computational Issues in the Geosciences
University of Padova, Italy, June 1720, 2013
Coorganizer of MiniSymposium: Dynamics of Nonlinear Flows in Porous Media: Analysis and Applications: Part I, Part II and Part III 
AMS 2012 Fall Western Sectional Meeting
University of Arizona, Tucson, AZ, October 2728, 2012 
AMS 2012 Central Fall Sectional Meeting
University of Akron, Akron, OH, October 2021, 2012 
The 9th AIMS Conference on Dynamical Systems, Differential Equations and Applications
July 1  5, 2012. Orlando, Florida  SIAM Conference on Analysis of Partial Differential Equations
San Diego, CA, November 1417, 2011
Coorganizer of MiniSymposium: Partial Differential Equations for Nonlinear Processes in Porous Media: Part I and Part II  34th Annual Texas Differential Equations Conference
March 2627, 2011, University of TexasPan American, Edinburg, TX 
AMS 2010 Fall Western Section Meeting
Los Angeles, CA, October 910, 2010 
AMS 2009 Spring Western Section Meeting
San Francisco, CA, April 2526, 2009  The 7th AIMS International Conference on Dynamical Systems and Differential Equations
Arlington, TX, May 1821, 2008  SIAM Conference on Analysis of Partial Differential Equations
December 1012, 2007, Mesa, Arizona  Nonlinear Dynamics and PDE MiniConference
Arizona State University, Tempe, AZ, November 1920, 2007  AMS 2007 Fall Southeastern Meeting
Murfreesboro, TN, November 34, 2007  The 3rd Symposium on Analysis & PDEs
Purdue University, West Lafayette, IN, May 2730, 2007  CMUChile Workshop on New Developments in Partial Differential
Equations I
Carnegie Mellon University, Pittsburgh, PA, May 2124, 2007 
AMS 2007 Spring Central Section Meeting
Oxford, OH, March 1617, 2007 
AMS 2007 Spring Southeastern Section Meeting
Davidson, NC, March 34, 2007 
AMS 2005 Spring Southeastern Sectional Meeting
Bowling Green, KY, March 1819, 2005 
SIAM Conference on Analysis of Partial Differential Equations
Houston, TX December 68, 2004 
AMS 2004 Spring Western Sectional Meeting
Los Angeles, CA, April 34, 2004
Presentations
 Overall talks: 2013, 2018
 Asymptotic expansions: 2017a, 2017b, 2017c
 Normal form for NavierStokes equations: 2007, 2011, 2015
 Forchheimer equations in porous media: 2009a, 2009b, 2010, 2013, 2014, 2017
 GeoPhysical fluid dynamics: 2006, 2007, 2008, 2012
 Statistical solutions to NavierStokes equations: 2007,
Profile The unexamined life is not worth living.  Socrates
Education
 2002  2005 Texas A&M University, College Station, Texas, Ph.D., Mathematics
 2000  2002 Indiana University, Bloomington, Indiana, Graduate student in Mathematics
 1998  2000 Arizona State University, Tempe, Arizona, M.A., Mathematics
 1997  1998 National University, Hochiminh City, Vietnam, Graduate student in Mathematics
 1993  1997 National University, Hochiminh City, Vietnam, B.S., Mathematics and Computer Science
 1993  1997 National University, Hochiminh City, Vietnam, B.S., Technology of Information.
Employment
 9.2014  present, Associate professor, Texas Tech University, Lubbock, Texas
 9.2008  8.2014, Assistant professor, Texas Tech University, Lubbock, Texas
 9.2005  5.2008, Dunham Jackson assistant professor, University of Minnesota, Minneapolis, Minnesota
 6.2004  12.2004, Teaching assistant, Texas A&M University, College Station, Texas
 9.2000  8.2002, Associate instructor, Indiana University, Bloomington, Indiana
 9.1998  8.2000, Teaching assistant and research assistant, Arizona State University, Tempe, Arizona
 9.1997  8.1998, Instructor, National University, Hochiminh City, Vietnam
Links All science requires mathematics.  Roger Bacon

Papers/Preprints

Space science

Science journals