Profile The unexamined life is not worth living.  Socrates
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
Teaching The only good is knowledge and the only evil is ignorance.  Socrates
Spring 2024
 MATH5099007. Partial Differential Equations II. (Graduate course, Ph.D. Prelim.)
 MATH4354001. Differential equations II.
Previous semesters
Old Webwork is on http://sibilant.math.ttu.edu Fall 2023. MATH5332001. Partial Differential Equations I. (Ph.D. Prelim.)
 Fall 2023. MATH4354001. Differential equations II.
 Fall 2022. MATH 5099007. Methods in Partial Differential Equations.
 Spring 2022. MATH3350012. Higher Mathematics for Engineers and Scientists I.
 Spring 2022. MATH3350111. Higher Mathematics for Engineers and Scientists I.
 Fall 2021. MATH2450011. Calculus III with Applications.
 Fall 2021. MATH2450013. Calculus III with Applications.
 Spring 2021. MATH2450002 and MATH2450D01. Calculus III with Applications.
 Fall 2020. MATH3351001. Higher Mathematics for Engineers and Scientists II.
 Fall 2020. MATH2450011. Calculus III with Applications.
 Spring 2020. MATH3350021. Higher Mathematics for Engineers and Scientists I.
 Spring 2020. MATH3350022. Higher Mathematics for Engineers and Scientists I.
 Fall 2019 MATH4351001. Advanced Calculus II.
 Fall 2019 MATH2450022. Calculus III With Applications.
 Spring 2019. MATH5332001. Partial Differential Equations I. (Ph.D. Prelim.)
 Spring 2019. MATH4354002. Differential equations II.
 Fall 2018. MATH3354002. Differential equations I.
 Fall 2018. MATH3351002. Higher Mathematics for Engineers and Scientists II.
 Spring 2018. MATH3354001. Differential equations I.
 Spring 2018. MATH4354002. Differential equations II.
 Spring 2017. MATH3350013. Higher Mathematics for Engineers and Scientists I.
 Spring 2017. MATH3351001. Higher Mathematics for Engineers and Scientists II.
 Summer II, 2016. MATH3350202. Higher Mathematics for Engineers and Scientists I.
 Spring 2016. MATH5332001. Partial Differential Equations I. (Ph.D. Prelim.)
 Spring 2016. MATH3351002. Higher Mathematics for Engineers and Scientists II.
 Fall 2015. MATH3351004. Higher Mathematics for Engineers and Scientists II.
 Fall 2015. MATH3350016. Higher Mathematics for Engineers and Scientists I.
 Spring 2015. MATH5332001. Partial Differential Equations I. (Ph.D. Prelim.)
 Spring 2015. MATH4351001. Advanced Calculus II. (undergraduate math majors)
 Fall 2014. MATH4350002. Advanced Calculus I. (undergraduate math majors)
 Fall 2014. MATH1320030. College Algebra.
 Spring 2014. MATH3310002. Introduction to Mathematical Reasoning and Proof.
 Spring 2014. MATH2360008. Linear Algebra.
 Fall 2013. MATH1451H01. Calculus I With ApplicationsHonors.
 Fall 2013. MATH2360001. Linear Algebra.
 Spring 2013. MATH5099011. Partial Differential Equations III. (graduate level)
 Spring 2013. MATH4354001. Differential Equations II.
 Fall 2012. MATH5333. Partial Differential Equations II.
 Fall 2012. MATH2450010. Calculus III with Applications.
 Spring 2012. MATH5332. Partial Differential Equations.
 Spring 2012. MATH3351001. Higher Mathematics for Engineers and Scientists II.
 Fall 2011. MATH3350010. Higher Mathematics for Engineers and Scientists I.
 Fall 2011. MATH3350012. Higher Mathematics for Engineers and Scientists I.
 Spring 2011. MATH5341001. Functional Analysis II.
 Spring 2011. MATH5332001. Partial Differential Equations.
 Fall 2010. MATH5340001. Functional Analysis.
 Fall 2010. MATH2360002. Linear Algebra.
 Spring 2010. MATH4354001. Differential Equations II.
 Spring 2010. MATH1352026. Calculus II.
 Fall 2009. MATH3354002. Differential Equations I.
 Fall 2009. MATH1351026. Calculus I.
 Spring 2009. MATH3350010. Higher Mathematics for Engineers and Scientists I.
 Fall 2008. MATH3350008. Higher Mathematics for Engineers and Scientists I.
Research What we know is a drop, what we don't know is an ocean.  Isaac Newton
Research interest
 Partial differential equations
 Fluid dynamics
 Porous medium equations
 Dynamical systems
Publications
All papers are in peer reviewed journals. List in PDF. Here is a list of typos and corrections Luan Hoang, Asymptotic expansions with subordinate variables for solutions of the NavierStokes equations, 140, submitted. [Preprint]
 Luan Hoang, Michael S. Jolly, Intrinsic expansions in large Grashof numbers for the steady states of the NavierStokes equations, 125, submitted. [Preprint]
 Luan Hoang, A new form of asymptotic expansion for nonsmooth differential equations with timedecaying forcing functions, 139, submitted. [Preprint]
 Luan Hoang, Thinh Kieu, Anisotropic flows of Forchheimertype in porous media and their steady states, 135, submitted. [Preprint]
 Luan Hoang, On the finite time blowups for solutions of nonlinear differential equations, 129, submitted. [Preprint]
 Luan Hoang, Behavior near the extinction time for systems of differential equations with sublinear dissipation terms, 122, submitted. [Preprint]
 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), 311370. (DOI:10.2422/20362145.202109_004)
 Ciprian Foias, Luan Hoang, Michael S. Jolly, On Galerkin approximations of the NavierStokes equations in the limit of large Grashof numbers, Communications on Pure and Applied Analysis, Volume 23, Issue 2 (2024), 269303. (DOI:10.3934/cpaa.2024010)
 Luan Hoang, The NavierStokes 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)
 Luan Hoang, Longtime behavior of solutions of superlinear systems of differential equations, Dynamical Systems, Vol. 39, No. 1 (2024), 79107. (DOI:10.1080/14689367.2023.2234845)
 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), 949987. (DOI:10.55730/13000098.3405)
 Dat Cao, Luan Hoang, Thinh Kieu, Infinite series asymptotic expansions for decaying solutions of dissipative differential equations with nonsmooth nonlinearity, Qualitative Theory of Dynamical Systems, Volume 20, Issue 3 (2021), 62, 38 pp. (DOI:10.1007/s12346021005029) [SharedIt link]
 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)
 Dat Cao, Luan Hoang, Asymptotic expansions with exponential, power, and logarithmic functions for nonautonomous nonlinear differential equations, Journal of Evolution Equations, Volume 21, Issue 2, 11791225, 2021. (DOI:10.1007/s0002802000622w) [Share link]
 Luan Hoang, Asymptotic expansions for the Lagrangian trajectories from solutions of the NavierStokes equations, Communications in Mathematical Physics, Volume 383, Issue 2, 981995 (2021). (DOI:10.1007/s00220020038635) [Share link]
 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, JanuaryFebruary 2021, 109137. (DOI:10.1016/j.anihpc.2020.06.005)
 Dat Cao, Luan Hoang, Asymptotic expansions in a genral system of decaying functions for the NavierStokes equations, Annali di Matematica Pura ed Applicata, Vol. 199, No. 3 (June 2020), 10231072. (DOI:10.1007/s10231019009113)
 Dat Cao, Luan Hoang, Longtime asymptotic expansions for NavierStokes equations with powerdecaying forces, Proceedings of the Royal Society of Edinburgh: Section A Mathematics, Vol. 150, No.2 (April 2020), 569606. (DOI:10.1017/prm.2018.154)
 Luan Hoang, Thinh Kieu, Global estimates for generalized Forchheimer flows of slightly compressible fluids, Journal d'Analyse Mathematique, March 2019, Volume 137, Issue 1, 155. (DOI:10.1007/s1185401800645) [SharedIt link]
 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) 36173650. (DOI:10.1088/13616544/aabf05)
 Ciprian Foias, Luan Hoang, JeanClaude Saut, Navier and Stokes meet Poincaré and Dulac, J. Appl. Anal. Comput., Volume 8, Number 3, June 2018, 727763. (DOI:10.11948/2018.727) (survey)
 Luan Hoang, Vincent Martinez, Asymptotic expansion for solutions of the NavierStokes equations with nonpotential body forces, J. Math. Anal. Appl., Volume 462, Issue 1, (1 June 2018) 84113. (DOI:10.1016/j.jmaa.2018.01.065)
 Emine Celik, Luan Hoang, Thinh Kieu, Generalized Forchheimer flows of isentropic gases, J. Math. Fluid Mech., March 2018, Volume 20, Issue 1, 83115. (DOI:10.1007/s0002101603132)
 Luan Hoang, Eric Olson, James Robinson, Continuity of pullback and uniform attractors, J. Differential Equations, Volume 264, Issue 6, (15 March 2018) 40674093. (DOI:10.1016/j.jde.2017.12.002)
 Luan Hoang, Thinh Kieu, Interior estimates for generalized Forchheimer flows of slightly compressible fluids, Advanced Nonlinear Studies, 17(4), (2017) 739767. (DOI:10.1515/ans20166027)
 Luan Hoang, Vincent Martinez, Asymptotic expansion in Gevrey spaces for solutions of NavierStokes equations, Asymptotic Analysis (2017), vol. 104, no. 34, 167190. (DOI:10.3233/ASY171429)
 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)
 Emine Celik, Luan Hoang, Maximum estimates for generalized Forchheimer flows in heterogeneous porous media, J. Differential Equations, Volume 262, Issue 3 (5 February 2017), 21582195. (DOI:10.1016/j.jde.2016.10.043)
 Luan Hoang, Truyen Nguyen, Tuoc Phan, Local gradient estimates for degenerate elliptic equations, Advanced Nonlinear Studies, Volume 16, Issue 3 (Aug 2016), 479489. (DOI:10.1515/ans20155038)
 Emine Celik, Luan Hoang, Generalized Forchheimer flows in heterogeneous porous media, Nonlinearity, Vol. 29, No. 3 (March 2016), 11241155. (DOI:10.1088/09517715/29/3/1124)
 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), 476544. (Also in "Problemy Matematicheskogo Analiza" 81, August 2015, 121178.) (DOI:10.1007/s1095801525761)
 Luan Hoang, Eric Olson, James Robinson, On the continuity of global attractors, Proc. Amer. Math. Soc., Volume 143, Number 10 (2015), 43894395. (DOI:10.1090/proc/12598)
 Luan Hoang, Truyen Nguyen, Tuoc Phan, Gradient estimates and global existence of smooth solutions to a crossdiffusion system, SIAM Journal on Mathematical Analysis, Volume 47, Issue 3 (2015), 21222177. (DOI:10.1137/140981447)
 Luan Hoang, Akif Ibragimov, Thinh Kieu, A family of steady twophase generalized Forchheimer flows and their linear stability analysis, J. Math. Phys. 55, Issue 12 (2014), 123101:32pp. (DOI:10.1063/1.4903002)
 Luan Hoang, Thinh Kieu, Tuoc Phan, Properties of generalized Forchheimer flows in porous media, Problems of Mathematical Analysis, Vol. 76 (August 2014), 133194, and in Journal of Mathematical Sciences, Vol. 202 No. 2, October 2014, 259332. (DOI:10.1007/s1095801420452)
 Luan Hoang, Incompressible fluids in thin domains with Navier friction boundary conditions (II), J. of Math. Fluid Mech., Volume 15, Issue 2, June 2013, 361395. (DOI:10.1007/s0002101201230)
 Luan Hoang, Akif Ibragimov, Thinh Kieu, Onedimensional twophase generalized Forchheimer flows of incompressible fluids, J. Math. Anal. Appl., Volume 401, Issue 2, 15 May 2013, 921938. (DOI:10.1016/j.jmaa.2012.12.055)
 Luan Hoang, Akif Ibragimov, Qualitative study of generalized Forchheimer flows with the flux boundary condition, Adv. Diff. Eq., Volume 17, Numbers 56, May/June 2012, 511556.
 Ciprian Foias, Luan Hoang, JeanClaude Saut, Asymptotic integration of NavierStokes equations with potential forces. II. An explicit PoincaréDulac normal form, J. Funct. Anal., Vol. 260, Issue 10, (2011) 30073035. (DOI:10.1016/j.jfa.2011.02.005)
 Luan Hoang, Akif Ibragimov, Structural stability of generalized Forchheimer equations for compressible fluids in porous media, Nonlinearity, Volume 24, Number 1 / January 2011, 141. (DOI:10.1088/09517715/24/1/001)
 Luan Hoang, George Sell, NavierStokes equations with Navier boundary conditions for an oceanic model, J. Dyn. Diff. Eqn., Volume 22, Number 3 / September 2010, 563616. (DOI:10.1007/s1088401091897)
 Luan Hoang, Incompressible fluids in thin domains with Navier friction boundary conditions (I), J. of Math. Fluid Mech., Volume 12, Number 3 / August 2010, 435472. (DOI:10.1007/s0002100902972)
 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)
 Ciprian Foias, Luan Hoang, Eric Olson, Mohammed Ziane, The normal form of the NavierStokes equations in suitable normed spaces, Annales de l'Institut Henri Poincare  Analyse non lineaire, Volume 26, Issue 5, SeptemberOctober 2009, 16351673. (DOI:10.1016/j.anihpc.2008.09.003)
 Ciprian Foias, Luan Hoang, Basil Nicolaenko, On the helicity in 3D NavierStokes equations II: The statistical case, Comm. Math. Physics, Volume 290, Issue 2 (2009) 679717. (DOI:10.1007/s002200090827z)
 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) 25852594, (DOI:10.1016/j.jde.2008.01.024)
 Ciprian Foias, Luan Hoang, Basil Nicolaenko, On the helicity in 3D NavierStokes equations I: The nonstatistical case, Proc. London Math. Soc., Volume 94 Number 1 (January 2007) 5390. (DOI:10.1112/plms/pdl003)
 Ciprian Foias, Luan Hoang, Eric Olson, Mohammed Ziane, On the solutions to the normal form of the NavierStokes equations, Indiana Univ. Math. J., Vol. 55, No 2 (2006) 631686. (DOI:10.1512/iumj.2006.55.2830)
Work in progress
 On intrinsic asymptotic expansions for the NavierStokes equations, (with Michael S. Jolly), in preparation.
 Longtime dynamics of fluid flows in geophysical fluid models, (with Animikh Biswas, Vincent R. Martinez) 28 pages, in preparation.
 Different types of longtime asymptotic expansions for the NavierStokes equations, multiple projects, in preparation.
 On longtime 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.
 NavierStokes equations with small viscosity, in preparation.
 Book project with Ciprian Foias, JeanClaude Saut.
 NavierStokes 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, JeanClaude 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

Workshop: Quasilinear PDEs in Fluid II
Virtual, jointly organized by Japan, Korea, U.S., February 2021, 2022. 
The 44th SIAM Southeastern Atlantic Section Conference
Auburn University, Auburn, Alabama, September 1819, 2021. 
2021 Joint AMSMAA Mathematics Meetings
January 69, 2021. 
AMS 2020 Fall Central Sectional Meeting
September 1213, 2020. 
AMS 2019 Fall Eastern Sectional Meeting
Binghamton University, Binghamton, NY, October 1213, 2019.  The 4th Annual Meeting of SIAM Central States Section, Norman, Oklahoma, October 57, 2018.
 2017 Joint Mathematics Meetings, Atlanta, Georgia, January 47, 2017.
 The 11th AIMS Conference on Dynamical Systems,
Differential Equations and Applications
Orlando, Florida, July 1  5, 2016
Coorganizer of special session (SS108) "New Developments in Porous Media" Schedule of talks 
International Conference on Evolution Equations
in conjunction with the 31st annual Shanks Lecture
Vanderbilt University, Nashville, TN, May 1620, 2016 
46th Annual John H. Barrett Memorial Lectures
University of Tennessee, Knoxville, TN, May 1618, 2016  The 40th SIAM Southeastern Atlantic Section Conference (SIAMSEAS). Applied Mathematics.
University of Georgia, Athens, Georgia, March 1213, 2016  2016 Joint Methamatics Meeting
Seattle, Washington, January 6  9, 2016  SIAM Conference on Analysis of Partial Differential Equations
Scottsdale, Arizona, December 710, 2015
Coorganizer of Minisymposium: "Dynamics of Partial Differential Equations" Part I and Part II. Schedule and Abstracts  AMS 2015 Spring Western Sectional Meeting
University of Nevada, Las Vegas, Las Vegas, NV, April 18  19, 2015  The 10th AIMS Conference on Dynamical Systems,
Differential Equations and Applications
Madrid, Spain, July 7  11, 2014  Advances in Mathematical Fluid Mechanics, Stochastic and Deterministic Methods
Lisbon, Portugal, June 30  July 5, 2014  AMS 2014 Spring Central Sectional Meeting
Texas Tech University, Lubbock, TX, April 1113, 2014
Coorganizer of Special Session: NavierStokes Equations and Fluid Dyanmics [Photos]  SIAM conference on Analysis of Partial Differential Equations
Lake Buena Vista, Florida, December 710, 2013
Coorganizer of MiniSymposium: Elliptic and Parabolic Equations with Nonstandard Nonlinearity. Speakers and Talks
Invited talk in MiniSymposium: Global Attractors, Dissipative Dynamical Systems, and Turbulence  SIAM conference on Mathematical and Computational Issues in the Geosciences
University of Padova, Italy, June 1720, 2013
Coorganizer of MiniSymposium: Dynamics of Nonlinear Flows in Porous Media: Analysis and Applications: Part I, Part II and Part III 
AMS 2012 Fall Western Sectional Meeting
University of Arizona, Tucson, AZ, October 2728, 2012 
AMS 2012 Central Fall Sectional Meeting
University of Akron, Akron, OH, October 2021, 2012 
The 9th AIMS Conference on Dynamical Systems, Differential Equations and Applications
July 1  5, 2012. Orlando, Florida  SIAM Conference on Analysis of Partial Differential Equations
San Diego, CA, November 1417, 2011
Coorganizer of MiniSymposium: Partial Differential Equations for Nonlinear Processes in Porous Media: Part I and Part II  34th Annual Texas Differential Equations Conference
March 2627, 2011, University of TexasPan American, Edinburg, TX 
AMS 2010 Fall Western Section Meeting
Los Angeles, CA, October 910, 2010 
AMS 2009 Spring Western Section Meeting
San Francisco, CA, April 2526, 2009  The 7th AIMS International Conference on Dynamical Systems and Differential Equations
Arlington, TX, May 1821, 2008  SIAM Conference on Analysis of Partial Differential Equations
December 1012, 2007, Mesa, Arizona  Nonlinear Dynamics and PDE MiniConference
Arizona State University, Tempe, AZ, November 1920, 2007  AMS 2007 Fall Southeastern Meeting
Murfreesboro, TN, November 34, 2007  The 3rd Symposium on Analysis & PDEs
Purdue University, West Lafayette, IN, May 2730, 2007  CMUChile Workshop on New Developments in Partial Differential
Equations I
Carnegie Mellon University, Pittsburgh, PA, May 2124, 2007 
AMS 2007 Spring Central Section Meeting
Oxford, OH, March 1617, 2007 
AMS 2007 Spring Southeastern Section Meeting
Davidson, NC, March 34, 2007 
AMS 2005 Spring Southeastern Sectional Meeting
Bowling Green, KY, March 1819, 2005 
SIAM Conference on Analysis of Partial Differential Equations
Houston, TX December 68, 2004 
AMS 2004 Spring Western Sectional Meeting
Los Angeles, CA, April 34, 2004
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 NavierStokes equations: 2017, 2018a, 2018b, 2018c, 2019
 Normal form for NavierStokes 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 NavierStokes equations: 2007,
Links All science requires mathematics.  Roger Bacon

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