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 and Harmonic analysis.
Teaching
Seminars
Research
Selected Research Papers
The Boltzmann equation, Besov spaces, and optimal time decay rates in $\R^n_x$, with
Vedran Sohinger .PDF
The Vlasov-Poisson-Landau System in $\R^3_x$, with Keya Zhu . PDF
A non-local inequality and global existence,
with
Philip T. Gressman
and
Joachim Krieger . Adv. Math. ,
230 (2012), no. 2, 642--648. (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 . Indiana Univ. Math. J. ,
to appear, 18 pages, 2011PDF
Optimal time decay of the non cut-off Boltzmann equation in the whole space .
Kinetic and Related Models ,
5 (2012), no. 3, 583--613.
doi: 10.3934/krm.2012.5.583
PDF
Global solutions to a non-local diffusion equation with quadratic non-linearity,
with Joachim Krieger . Comm. P.D.E. ,
37 (2012), no. 4, 647--689.
doi: 10.1080/03605302.2011.6434378
PDF
Momentum Regularity and
Stability of the Relativistic Vlasov-Maxwell-Boltzmann System, with Yan Guo . Comm. Math. Phys. ,
310 (2012), no. 3, 649--673.
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 