Research interests and Publications

Gautam Iyer

Research interests

My main research interests are in the use of probabilistic methods to better understand fluid dynamics. My work in this direction has been the development and use of the stochastic-Lagrangian formulation, an exact probabilistic representation of the Navier-Stokes equations, which studies incompressible fluids in terms of a noisy flow map. Other recent interests include global existence questions for PDEs related to fluid dynamics, and mixing properties of incompressible flows.

Publications and Preprints

Note: 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.)
  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. To appear in Nonlinearity. 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).
  9. (with Alexei Novikov) The regularizing effects of resetting in a particle system for the Burgers' equation. (Preprint). PDF PS (Booklet).

Seminars I organise/attend

Links

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Last Modified: Tue 03 Nov 2009 11:13:43 AM EST