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. A local estimate of the gradient for nonlinear elliptic equations, (with Truyen Nguyen, Tuoc Phan,) 8pp, to be submitted.
  2. Generalized Forchheimer flows of isentropic gases, (with Emine Celik, Thinh Kieu,) 37pp, submitted for publication. [arXiv Preprint]
  3. Global estimates for generalized Forchheimer flows of slightly compressible fluids, (with Thinh Kieu,) 41pp, submitted for publication. [arXiv Preprint]
  4. Interior estimates for generalized Forchheimer flows of slightly compressible fluids, (with Thinh Kieu,) 31pp, submitted for publication. [IMA Preprint] [arXiv Preprint]

  5. Stability of solutions to generalized Forchheimer equations of any degree, (with Akif Ibragimov, Thinh Kieu, Zeev Sobol,) 50pp, 2015, Journal of Mathematical Sciences (via journal "Problems in Mathematical Analysis"), accepted.
  6. Gradient estimates and global existence of smooth solutions to a cross-diffusion system, (with Truyen Nguyen, Tuoc Phan,) 47pp, 2015, SIAM Journal on Mathematical Analysis, accepted. [arXiv Preprint]
  7. On the continuity of global attractors, (with Eric Olson, James Robinson,) 7pp, 2015, Proc. AMS, in press. http://dx.doi.org/10.1090/proc/12598 [arXiv Preprint]
  8. 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
  9. 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]
  10. 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).
  11. 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).
  12. 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.
  13. 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).
  14. 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).
  15. 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).
  16. 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).
  17. 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).
  18. 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).
  19. 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).
  20. 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).
  21. 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).
  22. 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

  • Attractors of autonomous and nonautonomous systems, (with Eric Olson, James Robinson,) manuscript, 10pp.
  • Generalized Forchheimer flows in heterogeneous porous media, (with Emine Celik, N. C. Phuc,) manuscript, 35pp.
  • Gevrey estimates for normal form of Navier-Stokes equations, (with Vincent Martinez,) in preparation
  • General fluid flows in porous media, (with Emine Celik, Akif Ibragimov, Thinh Kieu,) in preparation.
  • Generalized Forchheimer flows in geophysical fluid dynamics, (with Emine Celik, Thinh Kieu,) 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.
  • Estimates for nonhomogeneous nonlinear PDEs, (with Truyen Nguyen, Tuoc Phan,) 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.
  • 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, Vincent Martinez, 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.

Conferences

Seminars

Grants

Profile

Education

CV

Links