Research interests and Publications

Gautam Iyer

Research interests

I completed my Ph.D. in 2006 from the University of Chicago. My thesis advisor was (is) Peter Constantin. My main interests are in PDE's that arise from fluid dynamics, and how stochastic methods can be applied to better understand them.

Publications and Preprints

1. Transport in viscous rotating fluids. Communications in Mathematical Sciences Volume 2, Issue 4, December (2005) 673--684. PDF, PS (Booklet)
2. A Stochastic perturbation of inviscid flows. Communications in Mathematical Physics 266 (2006) no. 3, 631--645. PDF, PS (Booklet)
3. (with Peter Constantin) A stochastic Lagrangian representation of the $3$-dimensional incompressible Navier-Stokes equations. To appear in Communications on Pure and Applied Mathematics. PDF PS (Booklet).
4. A stochastic Lagrangian formulation of the incompressible Navier-Stokes and related transport equations. Ph.D. Thesis, University of Chicago (2006). PDF PS (Booklet).
5. (with Peter Constantin) Stochastic Lagrangian transport and generalized relative entropies. Communications in Mathematical Sciences 4 (2006), no. 4, 767--777. PDF PS (Booklet).
6. A stochastic Lagrangian proof of global existence of the Navier-Stokes equations for flows with small Reynolds number. To appear in Annales de l'Institut Henri Poincar\'e. Analyse Non Lin\'eaire. PDF PS (Booklet).
7. (with Jonathan Mattingly) A stochastic-Lagrangian particle system for the Navier-Stokes equations, (Preprint). PDF PS (Booklet).
8. (with Peter Constantin and Jiahong Wu) Global regularity for a modified critical dissipative quasi-geostrophic equation. To appear in Indiana Univ. Math. J.. PDF PS (Booklet).