Renormalization and Energy Conservation for the Axisymmetric Euler Equation

Explore the intricacies of axisymmetric Euler equations without swirl in this 48-minute lecture from the Hausdorff Trimester Program on Evolution of Interfaces. Delve into the motion of vortex rings in ideal fluids, examining well-posedness and qualitative properties of solutions. Compare and contrast these equations with planar two-dimensional Euler equations. Investigate renormalization results for vanishing viscosity solutions derived from Navier-Stokes equations and analyze the conservation of kinetic energy. Gain insights from the collaborative research of Christian Seis and Camilla Nobili in this comprehensive exploration of fluid dynamics and mathematical physics.