Jacob Bedrossian
Associate Professor
Department of Mathematics
Center for Scientific Computation and Mathematical Modeling
University of Maryland, College Park
Applied Mathematics, Statistics, and Scientific Computation (AMSC) program
Burgers Program for Fluid Dynamics
office: 4129 CSIC and 4413 MATH
mail:
Jacob Bedrossian
The University of Maryland
CSCAMM
4146 CSIC Building #406
Paint Branch Drive
College Park MD 20742-3289, USA
email: jacob-at-cscamm-dot-umd-dot-edu or jacob-at-math-dot-umd-dot-edu
Research interests
My research is focused on the mathematical analysis of PDEs arising in fluid mechanics and plasma physics. Recently, most of my work has focused on understanding mixing, nonlinear stability, and turbulence in fluid mechanics at high Reynolds number and Landau damping-related effects in kinetic theory in the collisionless limit with a specific interest to problems relevant to plasma physics.
My research is currently funded by an NSF CAREER grant and a Sloan Fellowship.
Preprints
- Jacob Bedrossian, Michele Coti Zelati, Sam Punshon-Smith, Franziska Weber. A sufficient condition for the Kolmogorov 4/5 law for stationary martingale solutions to the 3D Navier-Stokes equations. arXiv:1711.03668 2018
- Jacob Bedrossian, Michele Coti Zelati, Vlad Vicol Vortex axisymmetrization, inviscid damping, and vorticity depletion in the linearized 2D Euler equations, arXiv:1711.03668 2017
- Jacob Bedrossian Nonlinear echoes and Landau damping with insufficient regularity, arXiv:1605.06841 2016
- Jacob Bedrossian, Pierre Germain, Nader Masmoudi Dynamics near the subcritical transition of the 3D Couette flow II: Above threshold case , arXiv:1506.03721 2015
Publications
- Jacob Bedrossian Suppression of plasma echoes and Landau damping in Sobolev spaces by weak collisions in a Vlasov-Fokker-Planck equation, Annals of PDE. arXiv:1704.00425 2017
- Jacob Bedrossian, Pierre Germain, Nader Masmoudi Dynamics near the subcritical transition of the 3D Couette flow I: Below threshold case , Mem. of the AMS. arXiv:1506.03720 2015
- Jacob Bedrossian, Siming He Suppression of blow-up in Patlak-Keller-Segel via shear flows, SIAM J. Math. Anal.. arXiv:1609.02866 2016
- Jacob Bedrossian, Nader Masmoudi, Clement Mouhot Landau damping in finite regularity for unconfined systems with screened interactions , Comm. Pure Appl. Math.. arXiv:1604.05783 2016
- Jacob Bedrossian, Michele Coti Zelati Enhanced dissipation, hypoellipticity, and anomalous small noise inviscid limits in shear flows, Arch. Rat. Mech. Anal.. 2015 arXiv:1510.08098
- Jacob Bedrossian, Pierre Germain, Nader Masmoudi On the stability threshold for the 3D Couette flow in Sobolev regularity , Annals of Math.. 2015. arXiv:1511.01373.
- Jacob Bedrossian, Vlad Vicol, Fei Wang The Sobolev stability threshold for 2D shear flows near Couette , J. Nonlinear Science. 2016. arXiv:1604.01831
- Jacob Bedrossian, Michele Coti Zelati, and Nathan Glatt-Holtz Invariant measures for passive scalars in the small noise inviscid limit, Comm. Math. Phys.. arXiv:1505.07356 2015.
- Jacob Bedrossian, Nader Masmoudi and Clement Mouhot Landau damping: paraproducts and Gevrey regularity, Annals of PDE. arXiv:1311.2870 2013.
- Jacob Bedrossian, Nader Masmoudi and Vlad Vicol Enhanced dissipation and inviscid damping in the inviscid limit of the Navier-Stokes equations near the 2D Couette flow, Arch. Rat. Mech. Anal.. arXiv:1408.4754 2014.
- Jacob Bedrossian, Nader Masmoudi Inviscid damping and the asymptotic stability of planar shear flows in the 2D Euler equations, Publ. Math. l'IHES. arXiv:1306.5028 2013.
- Jacob Bedrossian Large mass global solutions for a class of L1-critical nonlocal aggregation equations and parabolic-elliptic Patlak-Keller-Segel models . Comm. Part. Diff. Eqns.. arXiv:1403.4124 2014.
- Jacob Bedrossian, Nader Masmoudi Existence, Uniqueness and Lipschitz Dependence for Patlak-Keller-Segel and Navier-Stokes in R2 with Measure-valued initial data. Arch. Rat. Mech. Anal.. arXiv:1205.1551 2012.
- Jacob Bedrossian, Robert V. Kohn Blister patterns and energy minimization in compressed thin films on compliant substrates. Comm. Pure Appl. Math.. arXiv:1304.0284 2013.
- Jacob Bedrossian, Inwon Kim Global Existence and Finite Time Blow-Up for Critical Patlak-Keller-Segel Models with Inhomogeneous Diffusion, arXiv:1108.5301. SIAM J. Math. Anal. 45.3 (2013): 934-964.
- Jonas Azzam, Jacob Bedrossian, Bounded Mean Oscillation and the Uniqueness of Active Scalar Equations, Trans. Amer. Math. Soc.. arXiv:1108.2735, 2011
- Jacob Bedrossian, Nancy Rodriguez Inhomogeneous Patlak-Keller-Segel models and Aggregation Equations with Nonlinear Diffusion in R^d. Disc. and Dyn. Sys. B.. arXiv:1108.5167, 2011.
- Jacob Bedrossian, Intermediate asymptotics for critical and supercritical aggregation equations and Patlak-Keller-Segel models. Comm. Math. Sci. arXiv:1009.6187, 2010.
- Jacob Bedrossian, Global minimizers for free energies of subcritical aggregation equations with degenerate diffusion Appl. Math. Lett.. arXiv:1009.5370, 2010.
- Jacob Bedrossian, Nancy Rodriguez, Andrea Bertozzi, Local and Global Well-Posedness for Aggregation Equations and Patlak-Keller-Segel Models with Degenerate Diffusion, Nonlinearity, Vol. 24, No. 6 (2011)
- Jacob Bedrossian, James H. von Brecht, Siwei Zhu, Eftychios Sifakis, Joseph M. Teran, A virtual node method for Poisson interface problems in irregular domains , Journal of Computational Physics, Volume 229, Issue 18, Pages 6405-6426 (2010)
- Christophe Geuzaine, Jacob Bedrossian, Xavier Antoine, An Amplitude Formulation to Reduce the Pollution Error in the Finite Element Solution of Time-Harmonic Scattering Problems, IEEE Transactions on Magnetics, Vol. 44, No. 4, 2008
Expository materials
- Vlad Vicol and I ran an MSRI summer school titled "Incompressible Fluid Flows at High Reynolds Number"; guest lectures were also made by Roman Shyvdkoy. Videos of the lectures as well as written notes can be found here.
- Jacob Bedrossian, Nader Masmoudi Asymptotic stability for the Couette flow in the 2D Euler equations , arXiv:1309.2035 2013 [Expository note on arXiv:1306.5028] To appear in Appl. Math. Res. Expr.
Seminars and current topics courses
- Spring 2017: Turbulence and stochastic fluid mechanics reading course; we have worked through Frisch's book on turbulence together with mathematically rigorous works on weak martingale solutions of the stochastically forced Navier-Stokes equations.
- Spring 2016: Stochastic fluid mechanincs reading course; we have worked through a variety of notes and works on the uniqueness of invariant measures for the 2D stochastically forced Navier-Stokes equations. Specifically, our aim was to get familiar with the work of Hairer and Mattingly on the topic.
- Fall 2015: Stochastic fluid mechanics reading course; we are mostly working through the book on 2D stochastically forceed Navier-Stokes by Kuksin and Shirikyan. Email me or Michele Coti Zelati...Next semester we will likely work through Hairer and Mattingly (and the works that led up to this one).
- Spring 2015: WiPs seminar: joint with the MFD group in the Courant institute at NYU, we are currently running a seminar on waves in plasma. The page can be found here ! Email Lise-Marie or myself if you would like more information, or simply show up at the seminar at CSCAMM or Courant (depending on your physical location).
Teaching
I am now part of the Applied Mathematics, Statistics and Scientific Computation (AMSC) program!
If you are a graduate or undergraduate student interested in finding an REU project or PhD adviser, feel free to contact me and perhaps we can find something. I am open to advising students interested in the analysis of PDE as well as students who may also interested in doing some computation. Likely topics will be focused in some aspect of fluid mechanics or kinetic theory, tailored by the student interests, my interests, and our mutual expertises
- Math 673 - PDE I (Graduate level). See Canvas at myelms.umd.edu for all of the course information, announcements and assignments, Fall 2016
- Math 674 - PDE II (Graduate level). See Canvas at myelms.umd.edu for all of the course information, announcements and assignments, Spring 2016
- Math 462 - Introduction to PDEs. See Canvas at myelms.umd.edu for all of the course information, announcements and assignments, Fall 2015
- Math 462 - Introduction to PDEs. See Canvas at myelms.umd.edu for all of the course information, announcements and assignments, Spring 2015
- Math 858A Special topics in analysis:Long time dynamics of kinetic equations
- Math 410 - Advanced Calculus. See Canvas at myelms.umd.edu for all of the course information, announcements and assignments, Fall 2014
- (NYU) Spring 2013, Honors Calculus II
- (NYU) Fall 2013, Honors Calculus I
- (NYU) Spring 2012 Honors Calculus II
- (NYU) Fall 2011, Calculus I
Summer MAPS-REU 2016
As part of the MAPS REU in the mathematics department, I am advising 5 students on projects related to mixing and dissipation in fluid mechanics. The students are working on a variety of analysis and computational PDE projects. The talented students are:
- William Golding
- Gareth Johnson
- Chloe Ondracek
- Charlie Parker
- Jenalee Reardon
We would like to acknowledge the University of Maryland supercomputing resources (http://www.it.umd.edu/hpcc) made available for conducting the research. We are specifically using resources available on the Deepthought2 cluster. I would also like to acknowledge the Sloan foundation for providing some funding related to the research.
Previous positions
NSF postdoctoral fellow and Cathleen Morawetz postdoctoral fellow at the Courant Institute of Mathematical Sciences at New York University, 2011-2014.
Education
Ph.D. UCLA 2011, jointly advised by Prof. Andrea Bertozzi and Prof. Joseph Teran.
M.S./B.S Case Western Reserve University 2007, M.S. advised by Prof. Christophe Geuzaine.