# Well-posedness of logarithmic spiral vortex sheets

@inproceedings{Cieslak2021WellposednessOL, title={Well-posedness of logarithmic spiral vortex sheets}, author={T. Cie'slak and Piotr Kokocki and Wojciech S. O.za'nski}, year={2021} }

We consider a family of 2D logarithmic spiral vortex sheets which include the celebrated spirals introduced by Prandtl (Vorträge aus dem Gebiete der Hydround Aerodynamik, 1922) and by Alexander (Phys. Fluids, 1971). We prove that for each such spiral the normal component of the velocity field remains continuous across the spiral. Moreover, we give a complete characterization of such spirals in terms of weak solutions of the 2D incompressible Euler equations. Namely, we show that a spiral gives…

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