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

Spring 2015

Previous semesters

Research

Interest

  • Partial differential equations, fluid dynamics.
  • Porous medium equations.

Publication

  1. Interior estimates for generalized Forchheimer flows of slightly compressible fluids, (with Thinh Kieu,) 31pp, submitted for publication. [IMA Preprint] [arXiv Preprint]
  2. 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]
  3. Stability of solutions to generalized Forchheimer equations of any degree, (with Akif Ibragimov, Thinh Kieu, Zeev Sobol,) 50pp, submitted for publication. [IMA Preprint]

  4. On the continuity of global attractors, (with Eric Olson, James Robinson,) 7pp, 2014, Proc. AMS, accepted. [arXiv Preprint]
  5. A family of steady two-phase generalized Forchheimer flows and their linear stability analysis, (with Akif Ibragimov, Thinh Kieu,) J. Math. Phys. 55, 123101:32pp (2014). DOI: 10.1063/1.4903002
  6. 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). [IMA Preprint] [arXiv Preprint]
  7. 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).
  8. 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).
  9. 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.
  10. 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).
  11. 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).
  12. 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).
  13. 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).
  14. 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).
  15. 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).
  16. 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).
  17. 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).
  18. 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).
  19. 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

  • Global estimates for generalized Forchheimer flows of slightly compressible fluids, (with Thinh Kieu,) manuscript, 35pp.
  • Forchheimer equations for compressible fluids, (with Emine Celik, Thinh Kieu,) manuscript, 40pp.
  • Attractors of autonomous and nonautonomous systems, (with Eric Olson, James Robinson,) in preparation, 10pp.
  • Generalized Forchheimer flows in heterogeneous porous media, (with Emine Celik, N. C. Phuc,) in preparation, 30pp.
  • Statistical study of Forchheimer flows, (with Thinh Kieu,) in preparation, 10pp.
  • Two-phase general Forchheimer flows of mixed compressible fluids, (with Akif Ibragimov, Thinh Kieu,) in preparation.
  • Inverse problems in medical imaging, (with Loc Nguyen,) 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 Emine Celik, 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.

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