- Most of my work can be found on Google Scholar, Research Gate, arXiv preprint, and MathSciNet.
Recent Preprints:
- Linear Landau damping in R^3
Proceedings of the JEDP, Aussois (2023) - Linear Landau damping for the Vlasov-Maxwell system in R^3 (w/ D. Han-Kwan and F. Rousset)
arxiv preprint. - Plasmons for the Hartree equations with Coulomb interaction (w/ Chanjin You)
arxiv preprint. - Landau damping and the survival threshold
arxiv preprint. - On nonlinear instability of Prandtl’s boundary layers: the case of Rayleigh’s stable shear flows (w/ E. Grenier)
J. Math. Pures et Appliquees, 184 (2024), 71-90. - The inviscid limit of Navier-Stokes equations for locally near boundary analytic data on an exterior circular domain (w/ Trinh T. Nguyen)
Communications in Math Physics, 405 (2024), no 36. - The Vlasov–Poisson–Landau system in the weakly collisional regime (w/ S. Chaturvedi and J. Luk)
Journal of AMS, 36 (2023), no. 4, 1103-1189.
- 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, 40 (2023), no.6, 1457-1485. - The inviscid limit for the 2d Navier-Stokes equations in bounded domains (w/ C. Bardos, Trinh T. Nguyen, E. Titi)
Kinetic and Related Models, 15 (2022), no. 3, 317-340 - Plasma echoes near stable Penrose data (w/ E. Grenier and I. Rodnianski)
SIAM J. Math. Anal., 54 (2022), no. 1, 940-953.
Landau damping for analytic and Gevrey data (w/ E. Grenier and I. Rodnianski)
Mathematical Research Letters, 28 (2021), no. 6, 1679-1702. - 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, 387 (2021), no. 3, 1405-1440. - Asymptotic stability of equilibria for screened Vlasov-Poisson systems via pointwise dispersive estimates (w/ D. Han-Kwan and F. Rousset)
Annals of PDE, 7 (2021), Paper No. 18, 37 pp. - Generators functions and their applications (w/ E. Grenier)
Proceedings of AMS, Series B, 8 (2021), 245-251. - 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 - 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.