Return to Colloquia & Seminar listing
The Navier-Stokes equations in the hyperbolic settingPDE and Applied Math Seminar
In this talk we investigate how the geometry of the underlying domain affects the solutions to the Navier-Stokes equations. In particular, we show how the hyperbolic setting can lead to surprising phenomena that is not present in the Euclidean case. This includes the questions of uniqueness and definitions of the solution spaces. We also present advantageous properties of the hyperbolic geometry that allow us to obtain results for problems that have not been within reach in the Euclidean setting such as the stationary Liouville problem in 3D and if time permits, the 2D exterior domain problem.