Luan Thach Hoang

Spring 2012

• MATH5332. Partial Differential Equations.


• MATH3351. Higher Mathematics for Engineers and Scientists II.

Previous semesters

• 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. Functional Analysis II. Section 001.
• Spring 2011. MATH5332. Partial Differential Equations. Section 001.
• Fall 2010. MATH5340. Functional Analysis. Section 001.
• Fall 2010. MATH2360. Linear Algebra. Section 002.
• Spring 2010. MATH4354. Differential Equations II. Section 001.
• Spring 2010. MATH1352. Calculus II. Section 026.
• Fall 2009. MATH3354. Differential Equations I. Section 002.
• Fall 2009. MATH1351. Calculus I. Section 026.
• Spring 2009. MATH3350. Higher Mathematics for Engineers and Scientists I. Section 010.
• Fall 2008. MATH3350. Higher Mathematics for Engineers and Scientists I. Section 008.

Interest

• Partial differential equations, fluid dynamics.

Publications

1. Qualitative study of generalized Forchheimer flows with the flux boundary condition, (with Akif Ibragimov), 2011, Adv. Diff. Eq., accepted, 46pp.
2. 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).
3. Structural stability of generalized Forchheimer equations for compressible fluids in porus media, (with Akif Ibragimov), Nonlinearity, Volume 24, Number 1 / January 2011, 1-41. (doi: 10.1088/0951-7715/24/1/001).
4. Navier-Stokes equations with Navier boundary conditions for an oceanic model, (with George Sell), JDDE, Volume 22, Number 3 / September 2010, 563-616. (doi: 10.1007 /s10884-010-9189-7).
5. 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).
6. Analysis of generalized Forchheimer equations of compressible fluids in porus media, (with Eugenio Aulisa, Lidia Bloshanskaya, Akif Ibragimov), J. Math. Phys. 50, Issue 10, 103102:44pp (2009). (doi:10.1063/1.3204977).
7. 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).
8. 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).
9. 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).
10. 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).
11. 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

• Incompressible fluids in thin domains with Navier friction boundary conditions (II), manuscript, 30pp.
• On the stability of generalized Forchheimer flows, (with Akif Ibragimov, Thinh Kieu, Zeev Sobol), manuscript, 50pp.
• One-dimensional two-phase Forchheimer flows, (with Akif Ibragimov, Thinh Kieu), in preparation.
• An interface problem between incompressible clear fluid and fluid in porous media, (with Constantin Onica), in preparation.
• Normalization for Navier--Stokes equations (part 4), 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 Truyen Nguyen, Tuoc Phan, 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

• 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

• Forchheimer equations in porous media: Part I, Part II, Part III, Part IV

Visits

• June-August, 2005 Department of Mathematics, Indiana University

Grants

• NSF Grant DMS-0908177.

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

• Web-based: html
• Printable copy: pdf

TTU links

• TTU Libraries, Personal librarian for Math
• AMS MathSciNet via TTU Library
• TTU Calendars

Mathematical links

• Red Raider Mini-Symposium 2009: Non-linear Analysis, PDEs and Applications
• Applied Math Seminar, Texas Tech University
• MathSciNet Search
• IMA Preprint Series
• Math Archive Preprints
• Math on the Web (AMS)
• Math Encyclopedia
• Lists of Mathematics Departments
• History of Mathematics
• Mathematics Genealogy

TEX on the web

• AMS Link
• The Not So Short Introduction to LaTeX2e (pdf), by Tobias Oetiker, Hubert Partl, Irene Hyna and Elisabeth Schlegl
• Hypertext Help with LaTeX

Other Links

• Indiana Univ. Math. J
• Invent. Math
• J. Amer. Math. Soc
• Trans. Amer. Math. Soc.
• SIAM J. Math. Anal