Homepage of Gautam Iyer

Assistant Professor

Contact Info

Mailing address

Current courses

Past courses?

Solutions from previous course websites are usually removed. Since I don't keep my previous course websites updated, some links may or may not work.

Misc.

Research interests

Using probabilistic methods to study fluid dynamics
Global existence for PDEs related to fluid dynamics
Mixing properties of incompressible flows

Support Acknowledgement

Support from the National Science Foundation, and the Center for Nonlinear Analysis is gratefully acknowledged.

Publications and preprints

(with Robert L. Pego and Arghir Zarnescu) Coercivity and stability results for an extended Navier-Stokes system PDF (1up) PDF (2up)
(with Konstantinos C. Zygalakis) Numerical studies of homogenization under a fast cellular flow PDF PS (Booklet)?.
(with Tomasz Komorowski, Alexei Novikov, Lenya Ryzhik) From homogenization to averaging in cellular flows PDF PS (Booklet)?.
(with Peter Constantin) A stochastic-Lagrangian approach to the Navier-Stokes equations in domains with boundary. Ann. Appl. Probab. (to appear) PDF PS (Booklet)?.
(with Alexei Novikov, Lenya Ryzhik and Andrej Zlatos) Exit times for diffusions with incompressible drift. SIAM J. Math. Anal. (to appear). PDF PS (Booklet)?.
(with Alexei Novikov) The regularizing effects of resetting in a particle system for the Burgers' equation. Ann. Probab. (to appear). PDF PS (Booklet)?.
(with Peter Constantin and Jiahong Wu) Global regularity for a modified critical dissipative quasi-geostrophic equation. Indiana Univ. Math. J. 57 (2008), no. 6, 2681--2692. PDF PS (Booklet)?.
(with Jonathan Mattingly) A stochastic-Lagrangian particle system for the Navier-Stokes equations. Nonlinearity 21 (2008), no. 11, 2537--2553.. PDF PS (Booklet)?.
A stochastic Lagrangian proof of global existence of the Navier-Stokes equations for flows with small Reynolds number. Ann. Inst. H. Poincaré Anal. Non Linéaire 26 (2009), no. 1, 181--189. PDF PS (Booklet)?.
(with Peter Constantin) Stochastic Lagrangian transport and generalized relative entropies. Commun. Math. Sci. 4 (2006), no. 4, 767--777. PDF PS (Booklet)?.
A stochastic Lagrangian formulation of the incompressible Navier-Stokes and related transport equations. Ph.D. Thesis, University of Chicago (2006). PDF PS (Booklet)?.
(with Peter Constantin) A stochastic Lagrangian representation of the $3$-dimensional incompressible Navier-Stokes equations. Comm. Pure Appl. Math. 61 (2008), no. 3, 330--345. PDF PS (Booklet)?.
A Stochastic perturbation of inviscid flows. Comm. Math. Phys. 266 (2006), no. 3, 631--645. PDF PS (Booklet)?.
Transport in viscous rotating fluids. Commun. Math. Sci. 2 (2004), no. 4, 673--684. PDF PS (Booklet)?.

Booklet printing (save trees!)

The "PS Booklet" files are designed to be printed on a duplex printer, and then cut or folded in half. It reduces the amount of paper used by a factor of 4, so if you plan on printing out any of these papers, please use the "PS Booklet" version. (To convert any PDF file into booklet form see here.)

Office	WEH 6121
Phone	(412) 268 8419
Email Email Replace "NoSPAM" with "math". gautam@NoSPAM.cmu.edu Public Key 03C4B6C8

Gautam Iyer