Seminar by Mads Kyed (Flensburg)
Speaker: Mads Kyed (Flensburg)
Title: Navier-Stokes equations: Steady flow around a two-dimensional rotating body.
Abstract: The Navier-Stokes equations is as system of partial differential equations that govern the flow of a viscous fluid. Well-posedness of the corresponding initial-value problem in a three-dimensional domain is a famous open (millennium) problem. Other open problems include the existence of a steady-state solution in a two-dimensional exterior domain. In the first half my talk in will review the knowns and unknowns in the mathematical theory of the Navier-Stokes equations, and discuss some recent trends. In the second half I will focus on the steady-state Navier-Stokes problem in a two-dimensional exterior domain, that is, the steady flow around a two-dimensional body. I will present some new results which show that this open problem becomes solvable if a rotation is imposed on the body, and I will discuss a singularity that appears as the angular velocity of the rotation tends to zero.