Photo Vu Hoang

Vu Hoang

     Department of Mathematics       
     University of Texas at San Antonio

     One UTSA Circle San Antonio,
     Texas 78249


Research Interests

     Partial Differential Equations, Mathematical Relativity, Relativistic Hydrodynamics, 
     Spectral Theory of Schr
oedinger and Periodic Operators, Mathematical Physics,
     Mathematical Biology

Undergraduate and Graduate Research Opportunities

     I offer research projects on various levels, mostly at the interface between Mathematics and applications in Physics/Biology.
     Please contact me if you are interested.

     Prerequisites: one of the following: Calculus, Multivariable Calculus, Differential Equations I or Real Analysis.

     Information for Undergraduate/Graduate Research

Hawking Mathematical Physics Club

     The Mathematical Physics Club is a place to have stimulating discussion about Math & Physics topics. Everybody is welcome
     and can bring up any topic. See Hawking Mathematical Physics Club  for more information.

CV pdf


  • German Research Foundation HO 5156/1-1, HO 5156/1-2
  • National Science Foundation  DMS-1614797 and DMS-1810687
  • UTSA Grants for Research Advancement and Transformation (GREAT)

Selected Publications

     Fluid mechanics

  • with T. Do, M. Radosz and X. Xu: One-dimensional model equations for hyperbolic fuid flow. Nonlinear Analysis: Theory, Methods & Applications, Volume 140, July 2016, Pages 1-11 (doi:10.1016/, (arXiv: 1508.00550v2). 
  • with M. Radosz: No local double exponential gradient growth for the 2D Euler equation. Trans. Am. Soc (2017). Published electronically on February 13, 2017, DOI:
  • with M. Radosz: Cusp formation for a nonlocal transport equation, Arch. Rational. Mech Anal, 224(3) pp 1021-103 doi:10.007/s00205-017-1094-3.
  • with B. Orcan-Ekmekci, M. Radosz, H. Yang: Blowup with vorticity control for a 2D model of the Boussinesq equations.  Journal of Differential Equations, Vol. 264 (12), p.7328-7356 (2018).
  • with M. Radosz: Singular solutions with vorticity control for a  nonlocal system of evolution equations.Preprint  (October  2016, 15 pages) arXiv:1610.08955,

   Spectral Theory/Mathematical Physics

  • with B.M. Brown, M. Plum, M. Radosz and I. Wood: Gap localization of TE-Modes by arbitrarily weak defects. Journal of the London Mathematical Society, vol 95, 942-962 (2017) (Preprint: arXiv:1511.03723, 20 pages).
  • with M. Brown, M. Plum and I. Wood: On the spectrum of waveguides in planar photonic bandgap structures. Proceedings of the Royal Society A, 2176 (vol 471), (2015). DOI:10.1098/rspa.2014.0673 (arXiv:1204.0998). 
  • with M. Radosz: Absence of bound states for waveguides in 2D periodic structures. Journal of Mathematical Physics 55, 3 (2014) (arXiv:1111.4578v4).
  • with M. Brown, M. Plum and I. Wood: Spectrum created by line defects in periodic structures. Mathematische Nachrichten, Vol. 287, No 7 (2014) (arXiv:1306.6256).
  • The Limiting Absorption Principle in a semi-infnite periodic waveguide. SIAM Journal on Applied Mathematics, Vol.71, No.3 (2011).
  • with M. Plum, Ch. Wieners: A computer-assisted proof for photonic band gaps. Zeitschrift fuer angewandte Mathematik und Physik, 60 (2009).
  • with M. Brown, M. Wood and I.Wood, On spectral bounds for photonic crystal waveguides, Inequalities and applications, 22-30, Inter. Ser. Numer. Math., 157, Birkhaeuser, Basel (2009).
  • with D. Hundertmark, J. Richter and S. Vugalter: Existence and absence of weakly coupled bound states for Schroedinger-type operators with arbitrary kinetic energies. To appear in Annales Henri Poincare 2019. (Preprint:  arXiv:1610.09891, 26 pages)
  •  with B.M. Brown, M. Plum, M. Radosz and I. Wood: Gap localization of TE-Modes by arbitrarily weak defects: multiband case. (Preprint: arxiv:1901.05102, 20 pages, 2019)
  •  with M. Radosz: On higher-order electrodynamics. (Preprint:, 41 pages, 2019).

Teaching at UTSA

    MAT 1214 (Calculus I), MAT 3613 (Differential Equations I), MAT 2214 (Multivariable Calculus), MAT 4213 (Real

     Analysis for Undergraduates), MAT 3013 (Foundations of Mathematics), MAT 4223 (Real Analysis II)
      Click here to view a list of classes I taught at the Karlsruhe Institute of Technology and at Rice University

Photo by: Xiaolu Zhang