Prandtl spirals revisited

Prandtl spirals were introduced by Prandtl as a model of a vortex detaching from the tip of a wing when the plane takes off.

Until very recently it was not clear what is the status of the object: is it a solution to the 2D Euler, a solution of an approximate problem or an approximate solution? Or simply rubbish (which was not highly probable due to the fact that it was Prandtl who found out such an object)?

 

Together with Piotrek Kokocki and Wojtek Ożański we understood that Prandtl spirals solve 2D Euler in a weak sense. Moreover, we calculated the velocity corresponding to Prandtl spirals. In an announced talk I will speak about the recent common paper Piotrek Kokocki and Przemek Kosewski, where we give a simpler and much more natural proof of the fact that Prandtl spirals solve 2D Euler in a weak sense. Our proof dates back to July 2025, so it is a fully organic proof. No machines involved.