Abstract
We show the the voricity distribution obtained by minimizing the induced drag on a wing, the so called Prandtl-Munk vortex sheet, is not a travelling-wave weak solution of the Euler equations, contrary to what has been claimed by a number of authors. Instead, it is a weak solution of a non-homogeneous Euler equation, where the forcing term represents a "tension" force applied to the tips. This is consistent with a heuristic arguement due to Saffman. Thus, the notion of weak solution captures the correct physical behavior in this case.
Citation
Milton C. Lopes Filho. Helena J. Nussenzeig Lopes. Max O. Souza. "On the Equation Satisfied by a Steady Prandtl-Munk Vortex Sheet." Commun. Math. Sci. 1 (1) 68 - 73, March 2003.
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