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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!.