Department
of Mathematics
Welcome to my home page. I am now an Associate Professor in the Department of Mathematics and an affiliated faculty member of the Applied Mathematics and Computational Science graduate program at the University of Pennsylvania .
My research focuses on the analysis of non-linear partial differential equations which arise in physical contexts. I have particular interests in the equations of gas dynamics and fluid flow, such as the Boltzmann equation and the incompressible Navier-Stokes equations. Recently, I've also been working on Free boundary problems, Harmonic analysis and Numerical simulations.
Teaching
Seminars
Research
Selected Research Papers
The Vlasov-Poisson-Landau System in $\R^3_x$, with Keya Zhu Submitted, 50 pages, 2012 (arXiv:1202.2471v1)PDF
A non-local inequality and global existence,
with
Philip T. Gressman
and
Joachim Krieger .
Adv. Math. , in press, 8 pages, 2012. (arXiv:1202.4088v1)
doi: 10.1016/j.aim.2012.02.017
PDF
On partial regularity of steady-state solutions to the 6D Navier-Stokes equations, with Hongjie Dong Submitted, 18 pages, 2011PDF
Optimal time decay of the non cut-off Boltzmann equation in the whole space
PDF
Global solutions to a non-local diffusion equation with quadratic non-linearity,
with Joachim Krieger ,
Comm. P.D.E. in press, 35 pages, 2010.
doi: 10.1080/03605302.2011.6434378
PDF
Momentum Regularity and
Stability of the Relativistic Vlasov-Maxwell-Boltzmann System, with Yan Guo ,
Comm. Math. Phys. in press, 21 pages, 2010.
doi: 10.1007/s00220-012-1417-z PDF
On the global existence for the Muskat problem ,
with
Peter Constantin ,
Diego Córdoba ,
and
Francisco Gancedo .
J. Eur. Math. Soc. in press, 31 pages, 2010
PDF
Optimal Large-Time Behavior of the Vlasov-Maxwell-Boltzmann System in the Whole Space ,
with
Renjun Duan .
Commun. Pure Appl. Math
64 (2011), no. 11, 1497--1546.
doi: 10.1002/cpa.20381
PDF
Sharp anisotropic estimates for the Boltzmann collision operator and its entropy production ,
with
Philip T. Gressman .
Adv. Math. 227 (2011),
no. 6,
2349-2384.
doi: 10.1016/j.aim.2011.05.005
PDF
Hilbert Expansion from the Boltzmann equation to relativistic Fluids ,
with
Jared Speck
Comm. Math. Phys. 304 (2011),
no. 1,
229-280.
doi: 10.1007/s00220-011-1207-z
PDF
Global Classical Solutions of the Boltzmann Equation without Angular Cut-off ,
with
Philip T. Gressman
J. Amer. Math. Soc. 24 (2011), no. 3, 771-847.
doi: 10.1090/S0894-0347-2011-00697-8
PDF
Optimal Time Decay of the Vlasov-Poisson-Boltzmann System in $\R^3$ ,
with
Renjun Duan Arch. Ration. Mech. Anal. 199 (2011), no. 1, 291-328.
doi: 10.1007/s00205-010-0318-6
PDF
More downloadable papers...
Support
I would like to gratefully acknowledge current and past support from the National Science Foundation (DMS-1200747 , DMS-0901463 ,
DMS-0602513 ) and the
Alfred P. Sloan Foundation .
My academic webpages have been hit
StatCounter .
Robert M. Strain 