"Singular perturbations in fluid mechanics: Analysis and computations"

Dr. Gung-Min Gie

Department of Mathematics, University of Louisville

Abstract: Singular perturbations occur when a small coefficient affects the highest order derivatives in a system of partial differential equations. From the physical point of view, singular perturbations generate thin layers located near the boundary of a domain, called boundary layers, where many important physical phenomena occur. In this talk, we introduce a methodology, based on the utilization of correctors as proposed by J.-L. Lions and R. Temam, and use systematically this method of correctors to analyze the boundary layers of certain singularly perturbed fluid equations. We also discuss how to implement effective numerical schemes for slightly viscous fluid equations where the boundary layer correctors play essential roles.

Key words: fluid mechanics, partial differential equations, singular perturbations, correctors.