Open Access
March 2003 On the Equation Satisfied by a Steady Prandtl-Munk Vortex Sheet
Milton C. Lopes Filho, Helena J. Nussenzeig Lopes, Max O. Souza
Commun. Math. Sci. 1(1): 68-73 (March 2003).


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.


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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.


Published: March 2003
First available in Project Euclid: 7 June 2005

zbMATH: 1080.76018
MathSciNet: MR1979844

Rights: Copyright © 2003 International Press of Boston

Vol.1 • No. 1 • March 2003
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