Mathematical Problems in Fluid Dynamics

University Of Chicago, Chicago IL

Investigators

Abstract

0101022 Constantin Theoretical interest and experimental efforts concerning Lagrangian particle analysis have been increasing in the last years. The proposed research is to develop an Eulerian-Lagrangian approach initiated very recently. A main object of study in this approach is a diffusive Lagrangian path inverse that allows a natural formulation, including a viscous analogue of the inviscid Cauchy formula. The solution is built using a product expansion near the identity transformation. It is proposed to study this construction and apply it to randomly forced flows. In addition, the study of quenching of flames by strong random flows in turbulent combustion is proposed. Fluids and plasmas exhibit many active scales of motion, and are notoriously difficult to compute and predict accurately. The reason is that the equations describing them are not well understood. It is proposed to study mathematically the processes of transport of momentum and heat under extreme conditions