Stochastic analysis and control of fluid flow problems have seen great mathematical advancement over past two decades. A vast number of physical and engineering systems are encompassed under various flow governing equations. Various applications lie in defense related problems, important one is aero-hydrodynamic drag reduction in aerial, surface and undersea vehicles. Other applications are in atmospheric and ocean data assimilation, plasma fusion and energy-environmental problems.
The aim of the school is to make students and researchers across various organizations working in fluid flow problems well acquainted with the basic and advanced topics in control of partial differential equations (PDEs) arising from fluid dynamics with special emphasis on Navier-Stokes equations in both deterministic and stochastic settings. In the first week, introductory topics from Navier-Stokes equations, stochastic analysis and control of PDEs will be introduced. This would help in building the background for the advanced topics to be covered later on. In the following two weeks, solvability, control and large deviations of Navier-Stokes equations in both deterministic and stochastic settings will be covered. Topics on stochastic Navier-Stokes equations and stochastic Landau-Lifschitz-Gilbert equation on manifolds will also be covered using tools from differential geometry and stochastic analysis.
The winter school will also comprise of one day discussion meeting where a number of Indian senior experts will be invited to present their recent works related to the theme of the school. The discussion meeting aims to overview open problems and possible pathways to tackle them. This would help to enhance research activity in this area within India with the help of foreign experts through collaborations and exchange programmes.