Christian Seis: Renormalization and energy conservation for the axisymmetric Euler equation

The lecture was held within the framework of the Hausdorff Trimester Program: Evolution of Interfaces.

Abstract:
We consider the axisymmetric Euler equations without swirl, which describe, for instance, the motion of vortex rings in ideal fluids. We will give a short overview on previous results concerning well-posedness and qualitative properties of solutions and discuss similarities and differences with the planar two-dimensional Euler equations. In the main part of the talk, we present renormalization results for vanishing viscosity solutions obtained from the Navier-Stokes equations and discuss the conservation of the kinetic energy. Joint work with Camilla Nobili.