# Publications

## Preprints (on arxiv)

1. Nonlinear stability of source defects in oscillatory media, with Beck, Sandstede, and Zumbrun.
2. Global magnetic confinement in a bounded interval for the $1\frac12$ dimensional Vlasov--Maxwell systems, with T. V. Nguyen and W. Strauss.
3. Spectral stability of Prandtl boundary layers: an overview, with Grenier and Guo, arXiv:1406.4452
4. Spectral instability of characteristic boundary layer flows, with Grenier and Guo, arXiv:1406.3862
5. Spectral instability of symmetric shear flows in a two-dimensional channel, with Grenier and Guo, arXiv 1402.1395

## Published Articles

1. Nonlinear stability of source defects in the complex Ginzburg-Landau equation, with M. Beck, B. Sandstede, and K. Zumbrun.
Nonlinearity, to appear.
2. Topography influence on the Lake equations in bounded domains, with C. Lacave and B. Pausader,
J. Math. Fluid Mech., to appear.
3. Linear Stability Analysis of a Hot Plasma in a Solid Torus, with W. A. Strauss
Arch. Ration. Mech. Anal., to appear. pdf file
4. 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
5. Boundary layers interactions in the plane parallel incompressible flows (with F. Sueur),
Nonlinearity, 25 (2012) 3327--3342. pdf file
6. 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
7. A note on the Prandtl boundary layers (with Y. Guo).
Comm. Pure Appl. Math., 64 (2011), no. 10, 1416--1438. pdf file
8. Multi-dimensional stability of Lax shocks in hyperbolic-elliptic coupled systems.
Journal of Differential Equations, 252 (2012), no. 1, 382--411. pdf file
9. Remarks on the ill-posedness of the Prandtl equation (with D. Gerard--Varet).
Asymptotic Analysis, 77 (2012), no. 1-2, 71--88. pdf file
10. Long-time stability of multi-dimensional noncharacteristic viscous boundary layers (with K. Zumbrun).
Comm. Math. Phys., 299 (2010), no. 1, 1--44. pdf file
11. On asymptotic stability of noncharacteristic viscous boundary layers.
SIAM J. Math. Anal., 42 (2010), no. 3, 1156--1178. pdf file
12. 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
13. 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
14. Stability of multi-dimensional viscous shocks for symmetric systems with variable multiplicities.
Duke Math. J. 150 (2009), no. 3, 577--614. pdf file
15. 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
16. 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
17. 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
18. 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
19. Everywhere regularity for degenerate cross diffusion systems (with D. Le).
Comm. in PDEs, 31 (2006), no. 1-3, 307--324. pdf file
20. Persistence for a class of triangular cross diffusion parabolic systems (with D. Le).
Adv. Non. Stud., 5 (2005), no. 4, 493--514. pdf file
21. 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
22. Shigesada-Kawasaki-Teramoto model on higher dimensional domains (with D. Le and L. Nguyen).
Elec. J. Diff. Eqs., 2003, No. 72. pdf file

## 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.

## 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).

## Lecture notes

.....updating.....