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