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

• Most of my work can be found on Google Scholar, Research Gate, arXiv preprint, and MathSciNet.

Recent Preprints:

• The inviscid limit of Navier-Stokes equations for locally near boundary analytic data on an exterior circular domain (w/ Trinh T. Nguyen)
  arxiv preprint.
• The inviscid limit for the 2d Navier-Stokes equations in bounded domains (w/ C. Bardos, Trinh T. Nguyen, E. Titi)
  Kinetic and Related Models, to appear.
• The Vlasov--Poisson--Landau system in the weakly collisional regime (w/ S. Chaturvedi and J. Luk)
  Journal of AMS, to appear.
• On the linearized Vlasov-Poisson system on the whole space around stable homogeneous equilibria (w/ D. Han-Kwan and F. Rousset)
  Communications in Math Physics, to appear.
• Plasma echoes near stable Penrose data (w/ E. Grenier and I. Rodnianski)
  SIAM J. Math. Anal., to appear.
• Landau damping for analytic and Gevrey data (w/ E. Grenier and I. Rodnianski)
  Mathematical Research Letters, to appear.
• Asymptotic stability of equilibria for screened Vlasov-Poisson systems via pointwise dispersive estimates (w/ D. Han-Kwan and F. Rousset)
  Annals of PDE, to appear.
• Green function for linearized Navier-Stokes around a boundary shear layer profile for long wavelengths (w/ E. Grenier)
  Annales de l'IHP, Analyse Non Lineaire, to appear
• Generators functions and their applications (w/ E. Grenier)
  Proceedings of AMS, Series B, to appear.
• Green function for linearized Navier-Stokes around a boundary layer: near critical layers (w/ E. Grenier)
  arxiv preprint.

I. Fluid Dynamics 

• Sharp bounds for the resolvent of linearized Navier Stokes equations in the half space around a shear profile (w/ E. Grenier)
  J. Diff. Eqs., 2020
• On global stability of optimal rearrangement maps (w/ H. Q. Nguyen).
  Arch. Ration. Mech. Anal., 2020
• $L^\infty$ instability of Prandtl layers (w/ E. Grenier)
  Annals of PDE, 2019
• On nonlinear instability of Prandtl's boundary layers: the case of Rayleigh's stable shear flows (w/ E. Grenier)
  J. Math. Pures et Appliquees, accepted 2019
• Linear inviscid damping and enhanced viscous dissipation of shear flows by using the conjugate operator method (w/ E. Grenier, F. Rousset, and A. Soffer).
  Journal of Functional Analysis, 2019.
• The inviscid limit of Navier-Stokes equations for vortex-wave data on R^2 (w/ Trinh T. Nguyen).
  SIAM J. Math. Anal., 2019.
• Green function of Orr Sommerfeld equations away from critical layers (w/ E. Grenier)
  SIAM J. Math. Anal., 2019.
• The inviscid limit of Navier-Stokes for analytic data on the half-space (w/ Trinh Nguyen)
  Arch. Ration. Mech. Anal., 2018.
• Sublayer of Prandtl boundary layers (w/ E. Grenier)
  Arch. Ration. Mech. Anal., 2018.
• The onset of instability in first order systems (w/ N. Lerner and B. Texier)
  J. Euro Math Society, 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, 2017.
• Prandtl boundary layer expansions of steady Navier-Stokes over a moving plate (w/ Y. Guo)
  Annals of PDEs, 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

• Onsager type conjecture and renormalized solutions for the relativistic Vlasov Maxwell system (w/ C. Bardos and N. Besse)
  Quarterly of Applied Mathematics, 2019.
• Long time estimates of the Vlasov-Maxwell system in the non-relativistic regime (w/ D. Han-Kwan and F. Rousset)
  Comm. Math. Phys., 2018
• On the kinetic equation in Zakharov's wave turbulence theory for capillary waves (w/ M.-B. Tran)
  SIAM J. Math. Anal., 2018.
• Uniform in time lower bound for solutions to a Quantum Boltzmann of bosons (w/ M.-B. Tran)
  Arch. Ration. Mech. Anal., 2018.
• The Maxwell-Boltzmann approximation for ion kinetic modeling (w/ C. Bardos, F. Golse, and R. Sentis)
  Physica D: Nonlinear Phenomena, 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. Nonlinear Waves

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