Publications

Most of my papers are on Arxiv
My publications on Mathscinet
Me on Google Scholar
Me on Research Gate

Publications


 

Fluid Dynamics(e.g., inviscid limit, Prandtl boundary layers, fluid instabilities): 

  • Ill-posedness of the hydrostatic Euler and singular Vlasov equations, with D. Han-Kwan, preprint 2015, pdf file.
  • Prandtl boundary layer expansions of steady Navier-Stokes over a moving plate, with Y. Guo, preprint 2014.  arXiv:1411.6984 pdf file. 
  • Remarks on the inviscid limit for the compressible flows, with C. Bardos, preprint 2014,  arXiv:1410.4952
  • Spectral stability of Prandtl boundary layers: an overview, with Grenier and Guo. Preprint 2014, arXiv:1406.4452
  • Spectral instability of characteristic boundary layer flows, with Grenier and Guo. Preprint 2014, arXiv:1406.3862
  • Spectral instability of symmetric shear flows in a two-dimensional channel, with Grenier and Guo. Preprint 2014, arXiv:1402.139
  • Topography influence on the Lake equations in bounded domains, with C. Lacave and B. Pausader, J. Math. Fluid Mech., to appear. pdf file. 
  • Boundary layers interactions in the plane parallel incompressible flows (with F. Sueur), Nonlinearity, 25 (2012) 3327--3342. pdf file
  • A note on the Prandtl boundary layers (with Y. Guo). Comm. Pure Appl. Math., 64 (2011), no. 10, 1416--1438. pdf file
  • Remarks on the ill-posedness of the Prandtl equation (with D. Gerard--Varet). Asymptotic Analysis, 77 (2012), no. 1-2, 71--88. pdf file

 

Plasma Physics (e.g., plasma confinement, stability theory of equilibria):

  • Ill-posedness of the hydrostatic Euler and singular Vlasov equations, with D. Han-Kwan, preprint 2015, pdf file (also listed above!)
  • Nonlinear instability of Vlasov-Maxwell systems in the classical and quasineutral limits, with D. Han-Kwan, arXiv:1506.08537
  • Global magnetic confinement for the 1.5D  Vlasov-Maxwell system, with T. V. Nguyen and W. Strauss. Kinetic and Related Models, to appear, 2014. arXiv:1410.3003 
  • Linear Stability Analysis of a Hot Plasma in a Solid Torus, with W. A. Strauss. Arch. Ration. Mech. Anal., to appear. pdf file
  • Stability analysis of collisionless plasmas with specularly reflecting boundary, with W. A. Strauss. SIAM J. Math. Anal., 45(2013), no. 2, 777--808. pdf file

 

 

Instability of first-order systems:

  • The onset of instability in first-order systems, with N. Lerner and B. Texier, arxiv 2015

 

Traveling waves in oscillatory media:

  • Nonlinear stability of source defects in oscillatory media, with Beck, Sandstede, and Zumbrun. preprint, 2014
  • Nonlinear stability of source defects in the complex Ginzburg-Landau equation, with M. Beck, B. Sandstede, and K. Zumbrun. Nonlinearity, to appear.  pdf file.
  • Toward nonlinear stability of sources via a modified Burgers equation (with M. Beck, B. Sandstede, and K. Zumbrun). Physica D, 241 (2012), no. 4, 382--392. pdf file

  

Shock Wave Theory:

  • Multi-dimensional stability of Lax shocks in hyperbolic-elliptic coupled systems. Journal of Differential Equations, 252 (2012), no. 1, 382--411. pdf file
  • Stability of radiative shock profiles for hyperbolic-elliptic coupled systems (with R. Plaza and K. Zumbrun). Phys. D, 239 (2010), no. 8, 428--453. pdf file
  • Stability of scalar radiative shock profiles (with C. Lattanzio, C. Mascia, R. Plaza, and K. Zumbrun). SIAM J. Math. Anal. 41 (2009/10), no. 6, 2165--2206. pdf file
  • Stability of multi-dimensional viscous shocks for symmetric systems with variable multiplicities. Duke Math. J. 150 (2009), no. 3, 577--614. pdf file

 

 Non-characteristic Boundary Layers for compressible flows: 

  • Long-time stability of multi-dimensional noncharacteristic viscous boundary layers (with K. Zumbrun). Comm. Math. Phys., 299 (2010), no. 1, 1--44. pdf file
  • On asymptotic stability of noncharacteristic viscous boundary layers. SIAM J. Math. Anal., 42 (2010), no. 3, 1156--1178. pdf file
  • Long-time stability of large-amplitude noncharacteristic boundary layers of general hyperbolic-parabolic conservation laws (with K. Zumbrun). J. Math. Pures Appl. (9) 92 (2009), no. 6, 547--598. pdf file
  • Spectral stability of noncharacteristic isentropic Navier--Stokes boundary layers (with N. Costanzino, J. Humpherys, and K. Zumbrun). Arch. Ration. Mech. Anal. 192 (2009), no. 3, 537--587. pdf file

 

Elliptic/parabolic regularity theory

  • Regularity and coexistence problems for strongly coupled elliptic systems (with D. Le and L. Nguyen). Indiana Univ. Math. J., 56 (2007), no. 4, 1749--1791 pdf file
  • Global attractors and uniform persistence for cross diffusion parabolic systems (with D. Le). Dyn. Sys. and Apps. 16 (2007), no. 2, 361--377. pdf file
  • Everywhere regularity for degenerate cross diffusion systems (with D. Le). Comm. in PDEs, 31 (2006), no. 1-3, 307--324. pdf file
  • Persistence for a class of triangular cross diffusion parabolic systems (with D. Le). Adv. Non. Stud., 5 (2005), no. 4, 493--514. pdf file
  • Global existence for a class of triangular parabolic systems on domains of arbitrary dimension (with D. Le). Proc. of AMS, 133(2005), 1985-1992. pdf file
  • Shigesada-Kawasaki-Teramoto model on higher dimensional domains (with D. Le and L. Nguyen). Elec. J. Diff. Eqs., 2003, No. 72. pdf file

 

Proceedings


T. Nguyen and K. Zumbrun, Long-time stability of noncharacteristic viscous boundary layers. S\'eminaire 2009-2010: \'Equations aux d\'eriv\'ees partielles (Polytechnique).

Theses


  1. Asymptotic stability of noncharacteristic viscous boundary layers, Ph.D. thesis, Indiana University, 2009. pdf file
  2. Cross diffusion systems, M.S. thesis, University of Texas at San Antonio, 2006. pdf file
  3. Semi-group theory and fractional power operators, B.S. thesis, Vietnam National University, HoChiMinh city, 2002.