Luan Thach Hoang

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

Current

• Fall 2026. MATH3354-001. Differential Equations I.


• Fall 2026. MATH3351-001. Higher Mathematics for Engineers and Scientists II

Previous semesters

Research interest

• Partial differential equations
• Fluid dynamics
• Porous medium equations
• Dynamical systems

Publications

1. Luan Hoang, Akif Ibragimov, Linear non-divergence parabolic equations in non-cylindrical space-time sets, 1-58, submitted. [Preprint]
2. Emine Celik, Luan Hoang, Thinh Kieu, A priori estimates for gaseous flows of Forchheimer-type in heterogeneous porous media, 1-43, submitted. [Preprint]
3. Luan Hoang, Asymptotic expansions with subordinate variables for solutions of the Navier-Stokes equations, 1-40, submitted. [Preprint]
4. Luan Hoang, Michael S. Jolly, An intrinsic expansion approach to the Galerkin approximations for the Navier-Stokes equations (with an appendix by Chengzhang Fu), Discrete and Continuous Dynamical Systems (2027), Vol. 59, 276-304. (DOI:10.3934/dcds.2026167)
5. Luan Hoang, Akif Ibragimov, Linear non-divergence elliptic equations in a bounded, infinitely winding planar domain, Complex Variables and Elliptic Equations (2026), 1-31, in press. (DOI:10.1080/17476933.2026.2630197)
6. Emine Celik, Luan Hoang, Thinh Kieu, On compressible fluid flows of Forchheimer-type in rotating heterogeneous porous media, Mathematical Methods in the Applied Sciences (2026), Vol. 46, No. 13, 15010-15055. (DOI:10.1002/mma.70807)
7. Luan Hoang, A new form of asymptotic expansion for non-smooth differential equations with time-decaying forcing functions, Differential Equations and Dynamical Systems (2026), Vol. 34, No. 3, 697-741. (DOI:10.1007/s12591-024-00703-z)
8. Luan Hoang, Akif Ibragimov, Asymptotic estimates for solutions of inhomogeneous non-divergence diffusion equations with drifts, Journal of Mathematical Analysis and Applications (2026), Vol. 560, No. 2, 130489 (34 pages). (DOI:10.1016/j.jmaa.2026.130489)
9. Luan Hoang, On the finite time blow-ups for solutions of nonlinear differential equations, Evolution Equations and Control Theory (2026), Vol. 20, 91-121. (DOI:10.3934/eect.2026022)
10. Luan Hoang, Akif Ibragimov, A class of anisotropic diffusion-transport equations in non-divergence form, Contemporary Mathematics. Fundamental Directions (2025), Vol. 71, No. 4, 663--685. (Russian) The English version is to appear in Journal of Mathematical Sciences. (DOI:10.22363/2413-3639-2025-71-4-663-685) [Preprint]
11. Luan Hoang, Behavior near the extinction time for systems of differential equations with sublinear dissipation terms, Electronic Journal of Differential Equations (2025), Vol. 2025, No. 08, 1-26. (DOI:10.58997/ejde.2025.08)
12. Luan Hoang, Thinh Kieu, Anisotropic flows of Forchheimer-type in porous media and their steady states, Nonlinear Analysis: Real World Applications (2025), Vol. 84, 104269 (30 pp). (DOI:10.1016/j.nonrwa.2024.104269)
13. Luan Hoang, Michael S. Jolly, Intrinsic expansions in large Grashof numbers for the steady states of the Navier-Stokes equations, Nonlineary (2024), Vol. 37, No. 12, 125008 (32 pp). (DOI:10.1088/1361-6544/ad84aa)
14. Luan Hoang, Asymptotic expansions about infinity for solutions of nonlinear differential equations with coherently decaying forcing functions, Annali della Scuola Normale Superiore di Pisa, Classe di Scienze (2024), Vol. XXV, No. 1 , 311-370. (DOI:10.2422/2036-2145.202109_004)
15. Ciprian Foias, Luan Hoang, Michael S. Jolly, On Galerkin approximations of the Navier-Stokes equations in the limit of large Grashof numbers, Communications on Pure and Applied Analysis (2024), Volume 23, Issue 2, 269-303. (DOI:10.3934/cpaa.2024010)
16. Luan Hoang, The Navier-Stokes equations with body forces decaying coherently in time, Journal of Mathematical Analysis and Applications, Vol. 531, Issue 2, Part 1 (2024), 127863 (39 pp). (DOI:10.1016/j.jmaa.2023.127863)
17. Luan Hoang, Long-time behaviour of solutions of superlinear systems of differential equations, Dynamical Systems, Vol. 39, No. 1 (2024), 79-107. (DOI:10.1080/14689367.2023.2234845)
18. Emine Celik, Luan Hoang, Thinh Kieu, Studying a doubly nonlinear model of slightly compressible Forchheimer flows in rotating porous media, Turkish Journal of Mathematics, Vol. 47, No. 3 (2023), 949-987. (DOI:10.55730/1300-0098.3405)
19. Dat Cao, Luan Hoang, Thinh Kieu, Infinite series asymptotic expansions for decaying solutions of dissipative differential equations with non-smooth nonlinearity, Qualitative Theory of Dynamical Systems, Volume 20, Issue 3 (2021), 62, 38 pp. (DOI:10.1007/s12346-021-00502-9) [SharedIt link]
20. Emine Celik, Luan Hoang, Thinh Kieu, Slightly compressible Forchheimer flows in rotating porous media, Journal of Mathematical Physics, Volume 62 (2021), Issue 7, 073101, 39 pp. (DOI:10.1063/5.0047754)
21. Dat Cao, Luan Hoang, Asymptotic expansions with exponential, power, and logarithmic functions for non-autonomous nonlinear differential equations, Journal of Evolution Equations, Volume 21, Issue 2, 1179-1225, 2021. (DOI:10.1007/s00028-020-00622-w)
22. Luan Hoang, Asymptotic expansions for the Lagrangian trajectories from solutions of the Navier-Stokes equations, Communications in Mathematical Physics, Volume 383, Issue 2, 981-995 (2021). (DOI:10.1007/s00220-020-03863-5)
23. Luan Hoang, Edriss Titi, Asymptotic expansions in time for rotating incompressible viscous fluids, Annales de l'Institut Henri Poincare - Analyse non lineaire, Volume 38, Issue 1, January-February 2021, 109-137. (DOI:10.1016/j.anihpc.2020.06.005)
24. Dat Cao, Luan Hoang, Asymptotic expansions in a genral system of decaying functions for the Navier-Stokes equations, Annali di Matematica Pura ed Applicata, Vol. 199, No. 3 (June 2020), 1023-1072. (DOI:10.1007/s10231-019-00911-3)
25. Dat Cao, Luan Hoang, Long-time asymptotic expansions for Navier-Stokes equations with power-decaying forces, Proceedings of the Royal Society of Edinburgh: Section A Mathematics, Vol. 150, No.2 (April 2020), 569-606. (DOI:10.1017/prm.2018.154)
26. Luan Hoang, Thinh Kieu, Global estimates for generalized Forchheimer flows of slightly compressible fluids, Journal d'Analyse Mathematique, March 2019, Volume 137, Issue 1, 1-55. (DOI:10.1007/s11854-018-0064-5) [SharedIt link]
27. Emine Celik, Luan Hoang, Thinh Kieu, Doubly nonlinear parabolic equations for a general class of Forchheimer gas flows in porous media, Nonlinearity, Vol. 31, No. 8 (2018) 3617-3650. (DOI:10.1088/1361-6544/aabf05)
28. Ciprian Foias, Luan Hoang, Jean-Claude Saut, Navier and Stokes meet Poincaré and Dulac, J. Appl. Anal. Comput., Volume 8, Number 3, June 2018, 727-763. (DOI:10.11948/2018.727) (survey)
29. Luan Hoang, Vincent Martinez, Asymptotic expansion for solutions of the Navier-Stokes equations with non-potential body forces, J. Math. Anal. Appl., Volume 462, Issue 1, (1 June 2018) 84-113. (DOI:10.1016/j.jmaa.2018.01.065)
30. Emine Celik, Luan Hoang, Thinh Kieu, Generalized Forchheimer flows of isentropic gases, J. Math. Fluid Mech., March 2018, Volume 20, Issue 1, 83-115. (DOI:10.1007/s00021-016-0313-2)
31. Luan Hoang, Eric Olson, James Robinson, Continuity of pullback and uniform attractors, J. Differential Equations, Volume 264, Issue 6, (15 March 2018) 4067-4093. (DOI:10.1016/j.jde.2017.12.002)
32. Luan Hoang, Thinh Kieu, Interior estimates for generalized Forchheimer flows of slightly compressible fluids, Advanced Nonlinear Studies, 17(4), (2017) 739-767. (DOI:10.1515/ans-2016-6027)
33. Luan Hoang, Vincent Martinez, Asymptotic expansion in Gevrey spaces for solutions of Navier-Stokes equations, Asymptotic Analysis (2017), vol. 104, no. 3-4, 167-190. (DOI:10.3233/ASY-171429)
34. Emine Celik, Luan Hoang, Akif Ibragimov, Thinh Kieu, Fluid flows of mixed regimes in porous media, Journal of Mathematical Physics, Volume 58 (2017), No. 2, 023102, 30 pp. (DOI:10.1063/1.4976195)
35. Emine Celik, Luan Hoang, Maximum estimates for generalized Forchheimer flows in heterogeneous porous media, J. Differential Equations, Volume 262, Issue 3 (5 February 2017), 2158-2195. (DOI:10.1016/j.jde.2016.10.043)
36. Luan Hoang, Truyen Nguyen, Tuoc Phan, Local gradient estimates for degenerate elliptic equations, Advanced Nonlinear Studies, Volume 16, Issue 3 (Aug 2016), 479-489. (DOI:10.1515/ans-2015-5038)
37. Emine Celik, Luan Hoang, Generalized Forchheimer flows in heterogeneous porous media, Nonlinearity, Vol. 29, No. 3 (March 2016), 1124-1155. (DOI:10.1088/0951-7715/29/3/1124)
38. Luan Hoang, Akif Ibragimov, Thinh Kieu, Zeev Sobol, Stability of solutions to generalized Forchheimer equations of any degree, Journal of Mathematical Sciences, Volume 210, Number 4 (2015), 476-544. (Also in "Problemy Matematicheskogo Analiza" 81, August 2015, 121-178.) (DOI:10.1007/s10958-015-2576-1)
39. Luan Hoang, Eric Olson, James Robinson, On the continuity of global attractors, Proc. Amer. Math. Soc., Volume 143, Number 10 (2015), 4389-4395. (DOI:10.1090/proc/12598)
40. Luan Hoang, Truyen Nguyen, Tuoc Phan, Gradient estimates and global existence of smooth solutions to a cross-diffusion system, SIAM Journal on Mathematical Analysis, Volume 47, Issue 3 (2015), 2122-2177. (DOI:10.1137/140981447)
41. Luan Hoang, Akif Ibragimov, Thinh Kieu, A family of steady two-phase generalized Forchheimer flows and their linear stability analysis, J. Math. Phys. 55, Issue 12 (2014), 123101:32pp. (DOI:10.1063/1.4903002)
42. Luan Hoang, Thinh Kieu, Tuoc Phan, Properties of generalized Forchheimer flows in porous media, 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)
43. Luan Hoang, 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)
44. Luan Hoang, Akif Ibragimov, Thinh Kieu, One-dimensional two-phase generalized Forchheimer flows of incompressible fluids, J. Math. Anal. Appl., Volume 401, Issue 2, 15 May 2013, 921-938. (DOI:10.1016/j.jmaa.2012.12.055)
45. Luan Hoang, Akif Ibragimov, Qualitative study of generalized Forchheimer flows with the flux boundary condition, Adv. Diff. Eq., Volume 17, Numbers 5-6, May/June 2012, 511-556. (DOI:10.57262/ade/1355703078)
46. Ciprian Foias, Luan Hoang, Jean-Claude Saut, Asymptotic integration of Navier-Stokes equations with potential forces. II. An explicit Poincaré-Dulac normal form, J. Funct. Anal., Vol. 260, Issue 10, (2011) 3007-3035. (DOI:10.1016/j.jfa.2011.02.005)
47. Luan Hoang, Akif Ibragimov, Structural stability of generalized Forchheimer equations for compressible fluids in porous media, Nonlinearity, Volume 24, Number 1 / January 2011, 1-41. (DOI:10.1088/0951-7715/24/1/001)
48. Luan Hoang, George Sell, Navier-Stokes equations with Navier boundary conditions for an oceanic model, J. Dyn. Diff. Eqn., Volume 22, Number 3 / September 2010, 563-616. (DOI:10.1007/s10884-010-9189-7)
49. Luan Hoang, 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)
50. Eugenio Aulisa, Lidia Bloshanskaya, Luan Hoang, Akif Ibragimov, Analysis of generalized Forchheimer equations of compressible fluids in porous media, J. Math. Phys. 50, Issue 10, 103102:44pp (2009). (DOI:10.1063/1.3204977)
51. Ciprian Foias, Luan Hoang, Eric Olson, Mohammed Ziane, The normal form of the Navier-Stokes equations in suitable normed spaces, 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)
52. Ciprian Foias, Luan Hoang, Basil Nicolaenko, On the helicity in 3D Navier-Stokes equations II: The statistical case, Comm. Math. Physics, Volume 290, Issue 2 (2009) 679-717. (DOI:10.1007/s00220-009-0827-z)
53. Luan Hoang, 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)
54. Ciprian Foias, Luan Hoang, Basil Nicolaenko, On the helicity in 3D Navier-Stokes equations I: The non-statistical case, Proc. London Math. Soc., Volume 94 Number 1 (January 2007) 53-90. (DOI:10.1112/plms/pdl003)
55. Ciprian Foias, Luan Hoang, Eric Olson, Mohammed Ziane, On the solutions to the normal form of the Navier-Stokes equations, Indiana Univ. Math. J., Vol. 55, No 2 (2006) 631-686. (DOI:10.1512/iumj.2006.55.2830)

Work in progress

• Qualitative theory for non-divergence parabolic and elliptic equations, (with Akif Ibragimov) multiple projects, in preparation.
• On intrinsic asymptotic expansions for the Navier-Stokes equations, (with Michael S. Jolly), in preparation.
• Forchheimer flows in porous media, (with Emine Celik and Thinh Kieu) multiple projects, in preparation.
• Long-time dynamics of fluid flows in geophysical fluid models, (with Animikh Biswas, Vincent R. Martinez) 28 pages, in preparation.
• Different types of long-time asymptotic expansions for the Navier-Stokes equations, multiple projects, in preparation.
• Asymptotic expansions, asymptotic behaviors for systems of nonlinear ODEs, multiple projects, in preparation.
• On finite degree of freedom for fluids, (with Emine Celik,) 10 pages, in preparation.
• Navier-Stokes equations with small viscosity, in preparation.
• Book project with Ciprian Foias, Jean-Claude Saut.
• Navier-Stokes 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, Michael S. Jolly, Thinh Kieu, Vincent Martinez, Truyen Nguyen, Eric Olson, Tuoc Phan, James Robinson, Jean-Claude Saut, Zeev Sobol, Edriss Titi, Mohammed Ziane
• In Memoriam: Ciprian Foias (Obituray and tribute), Basil Nicolaenko (2007 Memorial Distinguished Lectures), George R. Sell (2016 dedicated workshop)

Conferences

Presentations

• Overall talks: 2013, 2018
• Lagrangian trajectories of fluid flows 2020a, 2020b, 2020c, 2021
• Asymptotic expansions for ODEs 2017, 2019, 2021a, 2021b, 2021c
• Asymptotic expansions for Navier-Stokes equations: 2017, 2018a, 2018b, 2018c, 2019
• Normal form for Navier-Stokes 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 Navier-Stokes equations: 2007,

Grants

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