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On the existence of convex classical solutions to a generalized Prandtl-Batchelor free boundary problem

  • A. Acker
Article

Abstract.

Under reasonably general assumptions, we prove the existence of convex classical solutions for the Prandtl-Batchelor free boundary problem in fluid dynamics, in which a flow of constant vorticity density is embedded in a potential flow, with a vortex sheet of constant vorticity density as the flow interface. These results apply to Batchelor flows which are confined to a bounded, convex vessel, and for which the limiting interior flow-speed exceeds the limiting exterior flow-speed along the interface.

Key words. Fluid dynamics, free boundary problem, convex vorticity localization, Batchelor flow. 

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Copyright information

© Birkhäuser Verlag, Basel, 1998

Authors and Affiliations

  • A. Acker
    • 1
  1. 1.Department of Mathematics and Statistics, Wichita State University, Wichita, KS 67260-0033, U.S.A., e-mail: acker@twsuvmUSA

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