# Publications

Most of my papers are on Arxiv

My publications on Mathscinet

Me on Google Scholar

Me on Research Gate

## Publications

Fluid Dynamics:

- Green function for the linearized Navier-Stokes around a boundary layer: the unstable case, with E. Grenier.

Preprint, 2016. - Ill-posedness of the hydrostatic Euler and singular Vlasov equations, with D. Han-Kwan,
**Arch. Ration. Mech. Anal.,**to appear, pdf file. - Prandtl boundary layer expansions of steady Navier-Stokes over a moving plate, with Y. Guo,

preprint 2014. pdf file. - Remarks on the inviscid limit for the compressible flows, with C. Bardos,
**Contemporary Mathematics, AMS**, to appear. pdf file - Spectral stability of Prandtl boundary layers: an overview, with Grenier and Guo.
**Analysis (Berlin)**35 (2015), no. 4, 343-355. pdf file - Spectral instability of characteristic boundary layer flows, with Grenier and Guo.
**Duke Math J,**to appear. pdf file - Spectral instability of symmetric shear flows in a two-dimensional channel, with Grenier and Guo.
**Advances in Math,**to appear. pdf file - 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

Kinetic theory:

- Uniform in time lower bound for solutions to a Quantum Boltzmann of bosons, with M-B. Tran.

preprint, May 2016. pdf file - Instabilities in the mean field limit, with D. Han-Kwan
**Journal of Statistical Physics**, to appear. pdf file. - Ill-posedness of the hydrostatic Euler and singular Vlasov equations, with D. Han-Kwan,
**Arch. Ration. Mech. Anal.****,**to appear. pdf file (also listed above!) - Nonlinear instability of Vlasov-Maxwell systems in the classical and quasineutral limits, with D. Han-Kwan,
**SiAM J Math Analysis, to appear, pdf file** - Global magnetic confinement for the 1.5D Vlasov-Maxwell system, with T. V. Nguyen and W. Strauss.
**Kinetic and Related Models**, to appear, 2014. pdf file - 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,
**Journal of the European Math. Society**. to appear. pdf file

### Traveling waves in oscillatory media:

- Nonlinear stability of source defects in the complex Ginzburg-Landau equation, with M. Beck, B. Sandstede, and K. Zumbrun.
**Nonlinearity, t**o 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

- E. Grenier, Y. Guo, and T. Nguyen, on the spectral instability of parallel shear flows, Séminaire Laurent Schwartz — EDP et applications (2014-2015), Exp. No. 22, 14 p. pdf file
- T. Nguyen and K. Zumbrun, Long-time stability of noncharacteristic viscous boundary layers. Séminaire Équations aux dérivées partielles (Polytechnique) (2009-2010), Exp. No. 6, 15 p. . pdf file

## Lecture notes

.....updating.....

## Theses

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