Speaker : Prof. Volker Elling (University of Michigan) Self-similar vortex spiral solutions of the 2d incompressible Euler equations 2014-10-16 (Thu) 14:30 - 15:30 Auditorium, 6 Floor, Institute of Mathematics (NTU Campus) Vortex spirals are ubiquitous in fluid flow, for example as turbulent eddies or as trailing vortices at aircraft wings. We consider solutions of the 2d incompressible Euler equations that have vorticity stratifying into algebraic spirals. The solutions are selfsimilar: velocity $v(t,x)=t^{m-1}v^(t^{-m}x)$, for similarity exponent $\frac12. The key to the existence proof is a coordinate change which is implicit, depending on the a priori unknown solution. We will also discuss the importance of the program for showing non-uniqueness in the initial-value problem for the Euler equations.