The Inviscid Limit and Boundary Layer Theory for Stationary Navier-Stokes Flows

It is well known that viscous incompressible flows moving past solid bodies develop boundary layers, i.e., very thin regions near the body's boundary where the flow rapidly adjusts to the surrounding free stream flow. Boundary layers are ubiquitous: they develop around bodies moving in air or water, such as airplanes, ships, and cars, and near the ground as wind blows over buildings and land. This project aims to establish rigorous mathematical results regarding the stability of boundary layers, building upon recent mathematical advances made by the principal investigator and collaborators in recent years. These mathematical results will inform a diverse range of scientific applications, e.g., by providing simpler reduced models which capture the qualitative behavior of boundary layer flows that can then be used to generate accurate fluid dynamics simulations. This project is devoted to the rigorous mathematical analysis of boundary layers and the inviscid limit for two dimensional, stationary, incompressible Navier-Stokes flows. Three regimes are identified for study which correspond to three different qualitative behaviors of the flow. The first regime will study the stability of globally laminar, self-similar boundary layers. These boundary layers have been confirmed to remarkable accuracy in experiments. The second regime is that of reversed flows. These flows are observed after boundary layer separation. Mathematically, this regime will require the introduction of new techniques from mixed-type problems, free boundary problems, and many other PDE disciplines. The third regime consists of projects studying boundary layer separation, which is a singularity phenomenon observed in nature. Here, large tangential gradients require higher-order boundary layer models to be studied. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.