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Visit Toan Nguyen's blog: Snapshots in Mathematics!.

**Publications:**

**I. Boundary layers and related topics in fluids:**

- Linear inviscid damping and enhanced viscous dissipation of shear flows by using the conjugate operator method (w/ E. Grenier, F. Rousset, and A. Soffer).

pdf file, submitted. - $L^\infty$ instability of Prandtl layers (w/ E. Grenier)

pdf file, submitted. - On nonlinear instability of Prandtl's boundary layers: the case of Rayleigh's stable shear flows (w/ E. Grenier)

pdf file, submitted. - Sharp bounds on linear semigroup of Navier Stokes with boundary layer norms (w/ E. Grenier)

pdf file, submitted. - Green function for linearized Navier-Stokes around a boundary layer: near critical layers (w/ E. Grenier)

pdf file, submitted. - Green function for linearized Navier-Stokes around a boundary layer: away from critical layers (w/ E. Grenier)

pdf file, submitted. - The inviscid limit of Navier-Stokes for analytic data on the half-space (w/ Trinh Nguyen)

Arch. Ration. Mech. Anal., to appear 2018. - Sublayer of Prandtl boundary layers (w/ E. Grenier)

Arch. Ration. Mech. Anal., to appear 2018. - The onset of instability in first order systems (w/ N. Lerner and B. Texier)

J. Euro Math Society, to appear 2018 - The vanishing viscosity limit for 2D Navier-Stokes in a rough domain (w/ D. Gerard-Varet, C. Lacave, and F. Rousset)

J. Math. Pures et Appliquees, to appear 2017. - Prandtl boundary layer expansions of steady Navier-Stokes over a moving plate (w/ Y. Guo)

Annals of PDEs, to appear 2017 - Illposedness of the hydrostatic Euler and singular Vlasov equations (w/ Han-Kwan)

Arch. Ration. Mech. Anal., 221 (2016), no. 3, 1317-1344. - Remarks on the inviscid limit for compressible flows (w/ C. Bardos)

Contemporary Mathematics, AMS, 2016 - Spectral instability of characteristic boundary layer flows (w/ E. Grenier and Y. Guo)

Duke Math J., 165 (2016), no. 16, 3085-3146 - Spectral instability of symmetric shear flows in a two-dimensional channel (w/ E. Grenier and Y. Guo)

Advances in Math., 292 (2016), pp. 52--110. - Spectral stability of Prandtl boundary layers: an overview (w/ E. Grenier and Y. Guo)

Analysis (Berlin) 35 (2015), no. 4, 343-355. - Topography influence on the Lake equations in bounded domains (with C. Lacave and B. Pausader)

J. Math. Fluid Mech., 16 (2014), no. 2, 375--406. - A note on the Prandtl boundary layers (w/ Y. Guo)

Comm. Pure Appl. Math., 64 (2011), no. 10, 1416--1438. - Boundary layers interactions in the plane parallel incompressible flows (w/ F. Sueur)

Nonlinearity, 25 (2012) 3327--3342. - Remarks on the ill-posedness of the Prandtl equation (w/ D. Gerard-Varet)

Asymptotic Analysis, 77 (2012), no. 1-2, 71--88.

**II. Kinetic theory of gases:**

- Long time estimates of the Vlasov-Maxwell system in the non-relativistic regime (w/ D. Han-Kwan and F. Rousset)

Comm. Math. Phys., to appear 2018 - On the kinetic equation in Zakharov's wave turbulence theory for capillary waves (w/ M.-B. Tran)

SIAM J. Math. Anal., to appear 2018. - Uniform in time lower bound for solutions to a Quantum Boltzmann of bosons (w/ M.-B. Tran)

Arch. Ration. Mech. Anal., to appear 2018. - The Maxwell-Boltzmann approximation for ion kinetic modeling (w/ C. Bardos, F. Golse, and R. Sentis)

Physica D: Nonlinear Phenomena, to appear 2017. - Instabilities in the mean field limit (w/ Han-Kwan)

Journal of Statistical Physics, 162 (2016), no. 6, 1639-1653. - Illposedness of the hydrostatic Euler and singular Vlasov equations (w/ Han-Kwan, also listed above)

Arch. Ration. Mech. Anal., 221 (2016), no. 3, 1317-1344. - Instability of Vlasov-Maxwell systems in the classical and quasineutral limits (w/ Han-Kwan)

SIAM J. Math. Anal., 48 (2016), no. 5, 3444-3466 - Global magnetic confinement for the 1.5D Vlasov-Maxwell system (w/ T. Nguyen and W. Strauss)

Kinetic and Related Models, 8 (2015), no. 1, 153-168. - Stability Analysis of a Hot Plasma in a Solid Torus (w/ W. Strauss)

Arch. Ration. Mech. Anal., 211 (2014), no. 2, 619-672. - Stability analysis of collisionless plasmas with specularly reflecting boundary (w/ W. Strauss)

SIAM J. Math. Anal., 45(2013), no. 2, 777--808.

**III. Dynamics of nonlinear waves and coherent structures:**

- Nonlinear stability of source defects in oscillatory media (w/ M. Beck, B. Sandstede, and K. Zumbrun)

pdf file, submitted. - Nonlinear stability of source defects in the complex Ginzburg-Landau equation (w/ M. Beck, B. Sandstede, and K. Zumbrun)

Nonlinearity, 27 (2014) 739-786 - Toward nonlinear stability of sources via a modified Burgers (w/ M. Beck, B. Sandstede, and K. Zumbrun)

Physica D, 241 (2012), no. 4, 382--392. - Multi-dimensional stability of Lax shocks in hyperbolic-elliptic coupled systems

Journal of Differential Equations, 252 (2012), no. 1, 382--411. - On asymptotic stability of noncharacteristic viscous boundary layers

SIAM J. Math. Anal., 42 (2010), no. 3, 1156--1178 - Stability of multi-dimensional viscous shocks for symmetric systems with variable multiplicities

Duke Math. J. 150 (2009), no. 3, 577--614. - Long-time stability of multi-dimensional noncharacteristic viscous boundary layers (w/ K. Zumbrun)

Comm. Math. Phys., 299 (2010), no. 1, 1--44. - Stability of radiative shock profiles for hyperbolic-elliptic coupled systems (w/ R. Plaza and K. Zumbrun)

Physica D. 239 (2010), no. 8, 428--453. - Stability of scalar radiative shock profiles (w/ C. Lattanzio, C. Mascia, R. Plaza, and K. Zumbrun)

SIAM J. Math. Anal. 41 (2009/10), no. 6, 2165--2206. - 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. - 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.

**IV. Elliptic and 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 - Global attractors and uniform persistence for cross diffusion parabolic systems (with D. Le)

Dyn. Sys. and Apps. 16 (2007), no. 2, 361--377. - Everywhere regularity for degenerate cross diffusion systems (with D. Le)

Comm. in PDEs, 31 (2006), no. 1-3, 307--324. - Persistence for a class of triangular cross diffusion parabolic systems (with D. Le)

Adv. Non. Stud., 5 (2005), no. 4, 493--514. - Global existence for a class of triangular parabolic systems on domains of arbitrary dimension (with D. Le)

Proc. of AMS, 133(2005), 1985-1992. - Shigesada-Kawasaki-Teramoto model on higher dimensional domains (with D. Le and L. Nguyen)

Elec. J. Diff. Eqs., 2003, No. 72.

Back to Toan Nguyen's homepage.

Visit Toan Nguyen's blog: Snapshots in Mathematics!.