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

Fall 2024

• MATH4000-004 (MATH4351). Advanced Calculus II


• 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, Asymptotic expansions with subordinate variables for solutions of the Navier-Stokes equations, 1-40, submitted. [Preprint]
2. Luan Hoang, Michael S. Jolly, Intrinsic expansions in large Grashof numbers for the steady states of the Navier-Stokes equations, 1-25, submitted. [Preprint]
3. Luan Hoang, A new form of asymptotic expansion for non-smooth differential equations with time-decaying forcing functions, 1-39, submitted. [Preprint]
4. Luan Hoang, Thinh Kieu, Anisotropic flows of Forchheimer-type in porous media and their steady states, 1-35, submitted. [Preprint]
5. Luan Hoang, On the finite time blow-ups for solutions of nonlinear differential equations, 1-29, submitted. [Preprint]
6. Luan Hoang, Behavior near the extinction time for systems of differential equations with sublinear dissipation terms, 1-22, submitted. [Preprint]
7. 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, Vol. XXV, No. 1 (2024), 311-370. (DOI:10.2422/2036-2145.202109_004)
8. 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, Volume 23, Issue 2 (2024), 269-303. (DOI:10.3934/cpaa.2024010)
9. 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 pages). (DOI:10.1016/j.jmaa.2023.127863)
10. Luan Hoang, Long-time behavior of solutions of superlinear systems of differential equations, Dynamical Systems, Vol. 39, No. 1 (2024), 79-107. (DOI:10.1080/14689367.2023.2234845)
11. 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)
12. 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]
13. 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)
14. 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) [Share link]
15. 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) [Share link]
16. 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)
17. 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)
18. 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)
19. 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]
20. 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)
21. 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)
22. 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)
23. 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)
24. 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)
25. 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)
26. 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)
27. 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)
28. 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)
29. 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)
30. 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)
31. 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)
32. 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)
33. 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)
34. 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)
35. 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)
36. 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)
37. 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)
38. 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.
39. 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)
40. 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)
41. 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)
42. 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)
43. 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)
44. 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)
45. 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)
46. 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)
47. 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)
48. 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

• On intrinsic asymptotic expansions for the Navier-Stokes equations, (with Michael S. Jolly), 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.
• On long-time dynamics of the Lagrangian trajectories in viscous, incompressible fluids, in preparation.
• Asymptotic expansions, asymptotic behaviors for systems of nonlinear ODEs, multiple projects, in preparation.
• Studies of anisotropic Forchheimer flows in porous media, preliminary ideas.
• 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).