Toan T. Nguyen
Department of Mathematics
Member of Center for Interdisciplinary Mathematics
Member of the Fluid Dynamics Research Consortium
Penn State University
State College, PA 16803
Office: 238 McAllister
Telephone: (814) 863-4123
- I work at the interface between physics and the theory of partial differential equations. In recent years, I have worked on the Prandtl's boundary layer theory, the kinetic theory of plasmas, the dynamics of coherent structures, the stability theory of nonlinear waves, and the weak turbulence theory.
- A short cv of mine
- My Publications page
- My Blog: Snapshots in Mathematics! updating my new research, lecture notes, expository articles, and related activities.
- My work can also be found on Google Scholar, Research Gate, arXiv preprint, and MathSciNet.
Books and lecture notes:
- Stability of Prandtl's boundary layers, with E. Grenier, 300 pp., preliminary review for Springer Books, 2017.
- Lecture notes on Kinetic theory of gases, Topics course notes, Fall 2017 (in preparation, link to blog posts).
- Lecture notes on Boundary layers, Topics course notes, Spring 2015. (link to blog posts).
- My lecture in Graduate Student Seminar on Fluid Dynamics (for 1st and 2nd year grad students), Jan 2018: slides.
- My lecture in Graduate Student Seminar on Kinetic Theory of Gases (for 1st and 2nd year grad students), Jan 2017: slides.
Recent submitted papers in fluids:
- The inviscid limit of Navier-Stokes for analytic data on the half-space (w/ Trinh Nguyen)
- On nonlinear instability of Prandtl's boundary layers: the case of Rayleigh's stable shear flows (w/ E. Grenier)
- Sublayer of Prandtl boundary layers (w/ E. Grenier)
- Sharp bounds on linear semigroup of Navier Stokes with boundary layer norms (w/ E. Grenier)
- Green function for linearized Navier-Stokes around a boundary layer: near critical layers (w/ E. Grenier)
- Green function for linearized Navier-Stokes around a boundary layer: away from critical layers (w/ E. Grenier)
- The vanishing viscosity limit for 2D Navier-Stokes in a rough domain (w/ D. Gerard-Varet, C. Lacave, and F. Rousset)
Recent submitted papers in kinetic theory:
- Long time estimates of the Vlasov-Maxwell system in the non-relativistic regime (w/ D. Han-Kwan and F. Rousset)
- The Maxwell-Boltzmann approximation for ion kinetic modeling (w/ C. Bardos, F. Golse, and R. Sentis)
- On the kinetic equation in Zakharov's wave turbulence theory for capillary waves (w/ M.-B. Tran)
- Uniform in time lower bound for solutions to a Quantum Boltzmann of bosons (w/ M.-B. Tran)
Weekly working seminars that I organized and led:
- June 25-29, 2018: The XVII International Conference on Hyperbolic Problems, Penn State University
- June 2-3, 2018: Southern California Analysis and PDE Conference, UC San Diego
- May 14-18, 2018: The 80th birthday conference of Walter Strauss, Brown University
- April 10, 2018: PDE Seminar, Georgia Institute of Technology
- March 6, 2018: CNA Seminar, Carnegie Mellon University
- Dec 18-22, 2017: Workshop on Cosmology and Plasma Physics, Wolfgang Pauli Institute, Vienna