Department of Mathematics and Statistics
Texas Tech University
Box 41042
Lubbock, TX 79409-1042
Office MA 208
Phone (806) 834-3060
Fax (806) 742-1112
luan(dot)hoang(at)ttu(dot)edu
http://www.math.ttu.edu/~lhoang/

Teaching

Fall 2016

  • No teaching.

Previous semesters

Research

Interest

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

Publication

(All papers are in peer reviewed journals)
  1. Continuity of pullback and uniform attractors, (with Eric Olson, James Robinson,) 23pp, in revision. [arXiv Preprint]
  2. Fluid flows of mixed regimes in porous media, (with Emine Celik, Akif Ibragimov, Thinh Kieu,) 33pp, submitted. [arXiv Preprint]
  3. Doubly nonlinear parabolic equations for a general class of Forchheimer gas flows in porous media, (with Emine Celik, Thinh Kieu,) 31pp, submitted. [arXiv Preprint]
  4. Asymptotic expansion in Gevrey spaces for solutions of Navier-Stokes equations, (with Vincent Martinez,) 20pp, submitted. [arXiv Preprint]
  5. Maximum estimates for generalized Forchheimer flows in heterogeneous porous media. (with Emine Celik,) 28pp, submitted. [arXiv Preprint]
  6. Generalized Forchheimer flows of isentropic gases, (with Emine Celik, Thinh Kieu,) 37pp, submitted. [arXiv Preprint]
  7. Interior estimates for generalized Forchheimer flows of slightly compressible fluids, (with Thinh Kieu,) 32pp, submitted. [arXiv Preprint]

  8. Global estimates for generalized Forchheimer flows of slightly compressible fluids, (with Thinh Kieu,) 41pp, Journal d'Analyse Mathematique, accepted. [arXiv Preprint]

  9. Local gradient estimates for degenerate elliptic equations, (with Truyen Nguyen, Tuoc Phan,) Advanced Nonlinear Studies, Volume 16, Issue 3 (Aug 2016), pp. 479-489. (DOI: 10.1515/ans-2015-5038) [arXiv Preprint]
  10. 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)
  11. 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)
  12. 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)
  13. 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)
  14. 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)
  15. 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)
  16. 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)
  17. 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)
  18. 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.
  19. 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)
  20. 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)
  21. 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)
  22. 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)
  23. 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)
  24. 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)
  25. 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)
  26. 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)
  27. 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)
  28. 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.

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