## Teaching

### Fall 2014

- MATH533-001. Partial Differential Equations II. (For graduate students after Ph.D. Preliminary exam)
- MATH4350-002. Advanced Calculus. (For undergraduate math majors)
- MATH4350-030. College Algebra. (For undergraduate math majors)

### Previous semesters

- 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

### Interest

- Partial differential equatiosns, fluid dynamics.
- Porous medium equations.

### Publications

- Interior estimates for generalized Forchheimer flows of slightly compressible fluids, (with Thinh Kieu,) 31pp, submitted for publication. [IMA Preprint] [arXiv Preprint]
- Self-diffusion and cross-diffusion equations: W^{1,p}-estimates and global existence of smooth solutions, (with Truyen Nguyen, Tuoc Phan,) 48pp, submitted for publication. [arXiv Preprint]
- A family of steady two-phase generalized Forchheimer flows and their linear stability analysis, (with Akif Ibragimov, Thinh Kieu,) 33pp, submitted for publication. [IMA Preprint] [arXiv Preprint]
- Stability of solutions to generalized Forchheimer equations of any degree, (with Akif Ibragimov, Thinh Kieu, Zeev Sobol,) 50pp, submitted for publication. [IMA Preprint]
- On the continuity of global attractors, (with Eric Olson, James Robinson) 7pp, 2014, Proc. AMS, accepted. [arXiv Preprint]
- Properties of generalized Forchheimer flows in porous media, (with Thinh Kieu, Tuoc Phan,) "Problems of Mathematical Analysis", volume 76 (July-August 2014), and in "Journal of Mathematical Sciences", Vol. 202 No. 2, October, 2014, 259-332. [IMA Preprint] [arXiv Preprint]
- 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

- Inverse problems in medical imaging.
- Statistical study of Forchheimer flows.
- Attractors of autonomous and nonautonomous systems, with Eric Olson, James Robinson.
- Global estimates and continuous dependence for generalized Forchheimer flows of slightly compressible fluids, (with Thinh Kieu,) in preparation.
- Generalized Forchheimer flows in inhomogeneous porous media, (with Emine Celik, N. C. Phuc,) in preparation.
- Forchheimer equations for gas, (with Emine Celik, Thinh Kieu,) in preparation.
- Normalization for Navier-Stokes equations: Part 4, (with Ciprian Foias, Eric Olson,) in preparation.
- Navier-Stokes equations with Navier boundary conditions for thin spherical shells, (with George Sell,) in preparation, 20pp.
- Optimal partitioning, (with Alexander Yu. Solynin,) in preparation.
- Convergence of a numerical algorithm for control systems, (with Eugenio Aulisa and David Gilliam,) in preparation.
- Navier-Stokes equations with Navier boundary conditions in thin domains: The reduced problem, (with George Sell,) in preparation.
- Other projects under discussion with Akif Ibragimov, Thinh Kieu, Linh Nguyen, Loc Nguyen, Truyen Nguyen, Eric Olson, Tuoc Phan, James Robinson, Tsuyoshi Yoneda.

### Theses/Dissertation

- Asymptotic expansions of the regular solutions to the 3D Navier-Stokes equations and applications to the analysis of the helicity. Ph.D. dissertation, 2005. [TAMU Library copy]
- Blowup versus regularity in the three dimensional Euler and Navier-Stokes equations. M.A. thesis, 2000.
- Holder continuity of the first derivatives of solutions of elliptic equations. B.S. thesis, 1997.

### Conferences

- 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

### Seminars

### Grants

- NSF Grants: DMS-0908177 (2009-2012), DMS-0931596 (2009), DMS-1412796 (2014-2017).

## 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.

### CV

- Printable copy: pdf

## Links

### Mathematical links

### TEX on the web

- AMS Link
- The Not So Short Introduction to LaTeX2e (pdf), by Tobias Oetiker, Hubert Partl, Irene Hyna and Elisabeth Schlegl