## Teaching

### Spring 2016

- MATH5332-001. Partial Differential Equations I. (For Math. Ph.D. Prelim. Exam.)
- MATH3351-002. Higher Mathematics for Engineers and Scientists II.

### Previous semesters

- Fall 2015. MATH3351-004. Higher Mathematics for Engineers and Scientists II.
- Fall 2015. MATH3350-016. Higher Mathematics for Engineers and Scientists I.
- Spring 2015. MATH5332-001. Partial Differential Equations I. (For Math. Ph.D. Prelim. Exam.)
- Spring 2015. MATH4351-001. Advanced Calculus II. (For undergraduate math majors)
- Fall 2014. MATH4350-002. Advanced Calculus I. (For undergraduate math majors)
- Fall 2014. MATH1320-030. College Algebra.
- Spring 2014. MATH3310-002. Introduction to Mathematical Reasoning and Proof.
- Spring 2014. MATH2360-008. Linear Algebra.
- Fall 2013. MATH1451-H01. Calculus I With Applications-Honors.
- Fall 2013. MATH2360-001. Linear Algebra.
- Spring 2013. MATH5099-011. Partial Differential Equations III. (graduate level)
- Spring 2013. MATH4354-001. Differential Equations II.
- Fall 2012. MATH5333. Partial Differential Equations II.
- Fall 2012. MATH2450-010. Calculus III with Applications.
- Spring 2012. MATH5332. Partial Differential Equations.
- Spring 2012. MATH3351-001. Higher Mathematics for Engineers and Scientists II.
- Fall 2011. MATH3350-010. Higher Mathematics for Engineers and Scientists I.
- Fall 2011. MATH3350-012. Higher Mathematics for Engineers and Scientists I.
- Spring 2011. MATH5341-001. Functional Analysis II.
- Spring 2011. MATH5332-001. Partial Differential Equations.
- Fall 2010. MATH5340-001. Functional Analysis.
- Fall 2010. MATH2360-002. Linear Algebra.
- Spring 2010. MATH4354-001. Differential Equations II.
- Spring 2010. MATH1352-026. Calculus II.
- Fall 2009. MATH3354-002. Differential Equations I.
- Fall 2009. MATH1351-026. Calculus I.
- Spring 2009. MATH3350-010. Higher Mathematics for Engineers and Scientists I.
- Fall 2008. MATH3350-008. Higher Mathematics for Engineers and Scientists I.

## Research

### Publication

(All papers are in peer reviewed journals)- Fluid flows of mixed regimes in porous media, (with Emine Celik, Akif Ibragimov, Thinh Kieu,) 33pp, submitted. [arXiv Preprint]
- Continuity of pullback and uniform attractors, (with Eric Olson, James Robinson,) 23pp, to be re-submitted. [arXiv Preprint]
- Doubly nonlinear parabolic equations for a general class of Forchheimer gas flows in porous media, (with Emine Celik, Thinh Kieu,) 31pp, submitted. [arXiv Preprint]
- Asymptotic expansion in Gevrey spaces for solutions of Navier-Stokes equations, (with Vincent Martinez,) 20pp, submitted. [arXiv Preprint]
- Maximum estimates for generalized Forchheimer flows in heterogeneous porous media. (with Emine Celik,) 28pp, submitted. [arXiv Preprint]
- Generalized Forchheimer flows of isentropic gases, (with Emine Celik, Thinh Kieu,) 37pp, submitted. [arXiv Preprint]
- Interior estimates for generalized Forchheimer flows of slightly compressible fluids, (with Thinh Kieu,) 32pp, submitted. [arXiv Preprint]
- Global estimates for generalized Forchheimer flows of slightly compressible fluids, (with Thinh Kieu,) 41pp, Journal d'Analyse Mathematique, accepted. [arXiv Preprint]
- Local gradient estimates for degenerate elliptic equations, (with Truyen Nguyen, Tuoc Phan,) 13pp, Advanced Nonlinear Studies, online April 2016, in press. (DOI: 10.1515/ans-2015-5038) [arXiv Preprint]
- Generalized Forchheimer flows in heterogeneous porous media, (with Emine Celik,) Nonlinearity, Vol. 29, No. 3 (March 2016), 1124-1155. (doi:10.1088/0951-7715/29/3/1124)
- 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), 476-544. (Also in "Problemy Matematicheskogo Analiza" 81, August 2015, pp. 121-178.) (doi: 10.1007/s10958-015-2576-1)
- On the continuity of global attractors, (with Eric Olson, James Robinson,) Proc. Amer. Math. Soc., Volume 143, Number 10 (2015), 4389-4395. (10.1090/proc/12598)
- Gradient estimates and global existence of smooth solutions to a cross-diffusion system, (with Truyen Nguyen, Tuoc Phan,) SIAM Journal on Mathematical Analysis, Volume 47, Issue 3, 2015, 2122-2177. (doi:10.1137/140981447)
- A family of steady two-phase generalized Forchheimer flows and their linear stability analysis, (with Akif Ibragimov, Thinh Kieu,) J. Math. Phys. 55, Issue 12, 123101:32pp (2014). (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, 133-194, and in Journal of Mathematical Sciences, Vol. 202 No. 2, October 2014, 259-332. (doi:10.1007/s10958-014-2045-2)
- Incompressible fluids in thin domains with Navier friction boundary conditions (II), J. of Math. Fluid Mech., Volume 15, Issue 2, June 2013, 361-395. (doi:10.1007/s00021-012-0123-0)
- One-dimensional two-phase generalized Forchheimer flows of incompressible fluids, (with Akif Ibragimov, Thinh Kieu,) J. Math. Anal. Appln., Volume 401, Issue 2, 15 May 2013, 921-938. (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 5-6, May/June 2012, 511-556.
- Asymptotic integration of Navier-Stokes equations with potential forces. II. An explicit Poincare-Dulac normal form, (with Ciprian Foias, Jean-Claude Saut,) J. Funct. Anal., Vol. 260, Issue 10, (2011) 3007-3035. (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, 1-41. (doi:10.1088/0951-7715/24/1/001)
- Navier-Stokes equations with Navier boundary conditions for an oceanic model, (with George Sell,) J. Dyn. Diff. Eqn., Volume 22, Number 3 / September 2010, 563-616. (doi:10.1007 /s10884-010-9189-7)
- Incompressible fluids in thin domains with Navier friction boundary conditions (I), J. of Math. Fluid Mech., Volume 12, Number 3 / August 2010, 435-472. (doi:10.1007/s00021-009-0297-2)
- 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 Navier-Stokes 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, September-October 2009, 1635-1673. (doi:10.1016/j.anihpc.2008.09.003)
- On the helicity in 3D Navier-Stokes equations II: The statistical case, (with Ciprian Foias, Basil Nicolaenko,) Comm. Math. Physics, Volume 290, Issue 2 (2009) 679-717. (doi:10.1007/s00220-009-0827-z)
- A basic inequality for the Stokes operator related to the Navier boundary condition, J. of Diff. Eqn., Volume 245, Issue 9, (1 November 2008) 2585-2594, (doi:10.1016/j.jde.2008.01.024)
- On the helicity in 3D Navier-Stokes equations I: The non-statistical case, (with Ciprian Foias, Basil Nicolaenko,) Proc. London Math. Soc., Volume 94 Number 1 (January 2007) 53-90. (doi:10.1112/plms/pdl003)
- On the solutions to the normal form of the Navier-Stokes equations, (with Ciprian Foias, Eric Olson, Mohammed Ziane,) Indiana Univ. Math. J., Vol. 55, No 2 (2006) 631-686.

### Work in progress

- Asymptotic expansion for solutions of the Navier-Stokes equations with non-potential body force, 16pp, manuscript.
- Fluid flows of mixed regimes in porous media. Part II., (with Emine Celik, Akif Ibragimov, Thinh Kieu,) in preparation.
- On the normal form and determining modes for NSE, (with Ciprian Foias, Cecilia Mondaini, Bingsheng Zhang,) in preparation.
- On NSE of rorating fluids, (with Ciprian Foias, Edriss Titi,) in preparation.
- Generalized Forchheimer flows in geophysical fluid dynamics, (with Emine Celik, Thinh Kieu,) in preparation.
- Generalized Forchheimer flows in heterogeneous porous media. Part III, (with Emine Celik, Thinh Kieu) in preparation.
- Mathematics in rhizosphere, (with Emine Celik, Thinh Kieu) in preparation.
- On dynamics and attractors III, (with Eric Olson, James Robinson,) in preparation.
- Fluid flows in anisotropic porous media, in preparation.
- On invariant nonlinear manifolds of NSE, (with Ciprian Foias, Jean-Claude Saut,) in preparation.
- Statistical study of Forchheimer flows, (with Thinh Kieu,) in preparation, 10pp.
- Continuous dependence for generalized Forchheimer flows of slightly compressible fluids, (with Thinh Kieu,) in preparation, 15pp.
- Navier-Stokes equations with Navier boundary conditions for thin spherical shells, (with George Sell,) in preparation, 20pp.
- Navier-Stokes equations with Navier boundary conditions in thin domains: The reduced problem, (with George Sell,) in preparation.

### Collaborators

- Other projects under discussion with Animikh Biswas, Emine Celik, Ciprian Foias, Akif Ibragimov, Thinh Kieu, Vincent Martinez, Cecilia Mondaini, Linh Nguyen, Loc Nguyen, Truyen Nguyen, Eric Olson, Tuoc Phan, James Robinson, Jean-Claude Saut, Edriss Titi, Tsuyoshi Yoneda, Bingsheng Zhang.

### Conferences

- The 11th AIMS Conference on Dynamical Systems,
Differential Equations and Applications

Orlando, Florida, July 1 - 5, 2016

Co-organizer of special session (SS108)*"New Developments in Porous Media"*Schedule of talks - IMA Special Workshop. Dynamics and Differential Equations.
**Dedicated to the memory of George R. Sell**

University of Minnesota, Minnesota, June 22-25, 2016 -
International Conference on Evolution Equations
in conjunction with the 31st annual Shanks Lecture

Vanderbilt University, Nashville, TN, May 16-20, 2016 -
46th Annual John H. Barrett Memorial Lectures

University of Tennessee, Knoxville, TN, May 16-18, 2016 - The 40th SIAM Southeastern Atlantic Section Conference (SIAM-SEAS). Applied Mathematics.

University of Georgia, Athens, Georgia, March 12-13, 2016 - 2016 Joint Methamatics Meeting

Seattle, Washington, January 6 - 9, 2016 - SIAM Conference on Analysis of Partial Differential Equations

Scottsdale, Arizona, December 7-10, 2015

Co-organizer of Mini-symposium:*"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 11-13, 2014

Co-organizer of Special Session:*Navier-Stokes Equations and Fluid Dyanmics*[ Photos ] - SIAM conference on Analysis of Partial Differential Equations

Lake Buena Vista, Florida, December 7-10, 2013

Co-organizer of Mini-Symposium:*Elliptic and Parabolic Equations with Nonstandard Nonlinearity.*Speakers and Talks

Invited talk in Mini-Symposium:*Global Attractors, Dissipative Dynamical Systems, and Turbulence* - SIAM conference on Mathematical and Computational Issues in the Geosciences

University of Padova, Italy, June 17-20, 2013

Co-organizer of Mini-Symposium:*Dynamics of Non-linear Flows in Porous Media: Analysis and Applications*: Part I, Part II and Part III -
AMS 2012 Fall Western Section Meeting

University of Arizona, Tucson, AZ, October 27-28, 2012 -
AMS 2012 Central Fall Section Meeting

University of Akron, Akron, OH, October 20-21, 2012, 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 14-17, 2011

Co-organizer of Mini-Symposium:*Partial Differential Equations for Non-linear Processes in Porous Media*: Part I and Part II - 34th Annual Texas Differential Equations Conference

March 26-27, 2011, University of Texas-Pan American, Edinburg, TX -
AMS 2010 Fall Western Section Meeting

Los Angeles, CA, October 9-10, 2010 -
AMS 2009 Spring Western Section Meeting

San Francisco, CA, April 25-26, 2009 - The 7th AIMS International Conference on Dynamical Systems and Differential Equations

Arlington, TX, May 18-21, 2008 - SIAM Conference on Analysis of Partial Differential Equations

December 10-12, 2007, Mesa, Arizona - Nonlinear Dynamics and PDE Mini-Conference

Arizona State University, Tempe, AZ, November 19-20, 2007 - AMS 2007 Fall Southeastern Meeting

Murfreesboro, TN, November 3-4, 2007 - The 3rd Symposium on Analysis & PDEs

Purdue University, West Lafayette, IN, May 27-30, 2007 - CMU-Chile Workshop on New Developments in Partial Differential
Equations I

Carnegie Mellon University, Pittsburgh, PA, May 21-24, 2007 -
AMS 2007 Spring Central Section Meeting

Oxford, OH, March 16-17, 2007 -
AMS 2007 Spring Southeastern Section Meeting

Davidson, NC, March 3-4, 2007 -
AMS 2005 Spring Southeastern Sectional Meeting

Bowling Green, KY, March 18-19, 2005 -
SIAM Conference on Analysis of Partial Differential Equations

Houston, TX December 6-8, 2004 -
AMS 2004 Spring Western Sectional Meeting

Los Angeles, CA, April 3-4, 2004

## Profile

### 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.