Robert M. Strain, PhD

Downloadable Publications and Preprints

Large Time Decay Estimates for the Muskat Equation, with Neel Patel.
Comm. P.D.E., (2017) doi: 10.1080/03605302.2017.1321661
On the Muskat problem: global in time results in 2D and 3D, with Peter Constantin, Diego Córdoba, Francisco Gancedo, and Luis Rodriguez-Piazza.
Amer. J. Math. (2016) doi: 10.1353/ajm.2016.0044
Axisymmetric flow of ideal fluid moving in a narrow domain: a study of the axisymmetric hydrostatic Euler equations, with Tak Kwong Wong.
J. Differential Equations (2016) doi: 10.1016/j.jde.2015.11.023
Strichartz estimates and moment bounds for the relativistic Vlasov-Maxwell system, with Jonathan Luk.
Arch. Ration. Mech. Anal. (2016) doi: 10.1007/s00205-015-0899-1
A new continuation criterion for the Vlasov-Maxwell system, with Jonathan Luk.
Comm. Math. Phys., 331 (2014), no. 3, 1005--1027.
doi: 10.1007/s00220-014-2108-8
Absence of splash singularities for the SQG sharp front and the multi-phase Muskat problem, with Francisco Gancedo.
Proc. Nat. Acad. Sci. U. S. A. 2014 111 (2) 635-639.
January 14, 2014: (arXiv:1309.4023) doi: 10.1073/pnas.1320554111
Commentary by Charles L. Fefferman
Spatially homogeneous Boltzmann equation for relativistic particles, with Seok-Bae Yun.
SIAM J. Math. Anal., 46 (2014), no. 1, 917--938.
doi: 10.1137/130923531
The Boltzmann equation, Besov spaces, and optimal time decay rates in $\R^n_x$, with Vedran Sohinger.
Advances in Math. (2014) (arXiv:1206.0027) doi: 10.1016/j.aim.2014.04.012
The Vlasov-Poisson-Landau System in $\R^3_x$, with Keya Zhu.
Arch. Ration. Mech. Anal.210 (2013), no. 2, 615-671.
(arXiv:1202.2471v1) doi: 10.1007/s00205-013-0658-0
Uniform $L^1$-stability of the relativistic Boltzmann equation near vacuum, with Seung-Yeal Ha and Eunhee Jeong.
Communications on Pure and Applied Analysis, 12 (2013), no. 2, 1141--1161.
doi: 10.3934/cpaa.2013.12.1141
On the global existence for the Muskat problem, with Peter Constantin, Diego Córdoba, and Francisco Gancedo.
J. Eur. Math. Soc., 5 (2013), no. 1, 201--227.
(arXiv:1007.3744) doi: 10.4171/JEMS/360
A non-local inequality and global existence, with Philip T. Gressman and Joachim Krieger.
Advances in Math., 230 (2012), no. 2, 642--648.
(arXiv:1202.4088v1) doi: 10.1016/j.aim.2012.02.017
Large-Time Decay of the Soft Potential relativistic Boltzmann equation in $\R^3_x$, with Keya Zhu.
Kinetic and Related Models, 5 (2012), no. 2, 383--415.
(arXiv:1106.1579v1) doi: 10.3934/krm.2012.5.383
On partial regularity of steady-state solutions to the 6D Navier-Stokes equations, with Hongjie Dong.
Indiana Univ. Math. J.61 (2012), 2211-2229.
(arXiv:1101.5580) doi: 10.1512/iumj.2012.61.4765
Optimal time decay of the non cut-off Boltzmann equation in the whole space.
Kinetic and Related Models, 5 (2012), no. 3, 583--613.
(arXiv:1011.5561) doi: 10.3934/krm.2012.5.583
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.
(arXiv:1012.2890) doi: 10.1080/03605302.2011.6434378
Momentum Regularity and Stability of the Relativistic Vlasov-Maxwell-Boltzmann System, with Yan Guo.
Comm. Math. Phys., 310 (2012), no. 3, 649--673.
(arXiv:1012.1158) doi: 10.1007/s00220-012-1417-z
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.
(arXiv:1006.3605) doi: 10.1002/cpa.20381
Sharp anisotropic estimates for the Boltzmann collision operator and its entropy production, with Philip T. Gressman.
Advances in Math. 227 (2011), no. 6, 2349-2384.
(arXiv:1007.1276) doi: 10.1016/j.aim.2011.05.005
Hilbert Expansion from the Boltzmann equation to relativistic Fluids, with Jared Speck.
Comm. Math. Phys.304 (2011), no. 1, 229-280.
(arXiv:1009.5033) doi: 10.1007/s00220-011-1207-z
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.
(arXiv:1011.5441) doi: 10.1090/S0894-0347-2011-00697-8
Coordinates in the relativistic Boltzmann theory.
Kinetic and Related Models Vol. 4, March 2011, No. 1, 345-359, special issue.
(arXiv:1011.5093) doi: 10.3934/krm.2011.4.345
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
Asymptotic Stability of the Relativistic Boltzmann Equation for the Soft Potentials.
Comm. Math. Phys.300 (2010), no. 2, 529-597.
doi: 10.1007/s00220-010-1129-1
Global Classical solutions of the Boltzmann equation with Long-Range interactions, with Philip T. Gressman.
Proc. Nat. Acad. Sci. U. S. A. 2010 107 (13), 5744-5749.
March 30, 2010: doi: 10.1073/pnas.1001185107
Global Newtonian limit for the Relativistic Boltzmann Equation near Vacuum.
SIAM J. Math. Anal.,42, Issue 4, pp. 1568-1601 (2010).
doi: 10.1137/090762695
Lower bounds on the blow-up rate of the axisymmetric Navier-Stokes equations II, with Chiun-Chuan Chen, Tai-Peng Tsai, and Horng-Tzer Yau.
Comm. P.D.E. 34 (2009), no. 3, 203 - 232.
doi: 10.1080/03605300902793956
Lower bound on the blow-up rate of the axisymmetric Navier-Stokes equations, with Chiun-Chuan Chen, Tai-Peng Tsai, and Horng-Tzer Yau.
Int. Math. Res. Not., (2008) Vol. 2008 published on March 14, 2008.
doi: 10.1093/imrn/rnn016
Exponential Decay for Soft Potentials Near Maxwellian, with Yan Guo .
Arch. Ration. Mech. Anal.187 (2008), no. 2, 287-339.
doi: 10.1007/s00205-007-0067-3
Spectral gap and coercivity estimates for linearized Boltzmann collision operators without angular cutoff, with Clément Mouhot.
J. Math. Pures Appl. 87 (2007), no. 5, 515-535.
doi: 10.1016/j.matpur.2007.03.003
On the Linearized Balescu-Lenard Equation.
Comm. P.D.E. 32 (2007), no. 10, 1551-1586.
doi: 10.1080/03605300601088609
The Vlasov-Maxwell-Boltzmann System in the Whole Space.
Comm. Math. Phys. 268 (2006), no. 2, 543-567.
doi: 10.1007/s00220-006-0109-y
Almost Exponential Decay Near Maxwellian, with Yan Guo.
Comm. P.D.E. 31 (2006), no. 3, 417-429.
doi: 10.1080/03605300500361545
Some Applications of an Energy Method in Collisional Kinetic Theory,
Phd Thesis, Brown University, Providence RI (2005)
Stability of the Relativistic Maxwellian in a Collisional Plasma, with Yan Guo .
Comm. Math. Phys. 251 (2004), no. 2, 263-320.
doi: 10.1007/s00220-004-1151-2

A few research links

Preprints on arXiv

Papers on MathSciNet (subscription required)

Short Vitae PDF

Bibliography PDF

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Links are not always up to date.

I would like to gratefully acknowledge current and past research support from the National Science Foundation (DMS-1500916, DMS-1200747, DMS-0901463, DMS-0602513) and the Alfred P. Sloan Foundation.

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