Journal of Mathematical Fluid Mechanics

, Volume 12, Issue 3, pp 321–334

Resolution of d’Alembert’s Paradox

  • Johan Hoffman
  • Claes Johnson

DOI: 10.1007/s00021-008-0290-1

Cite this article as:
Hoffman, J. & Johnson, C. J. Math. Fluid Mech. (2010) 12: 321. doi:10.1007/s00021-008-0290-1


We propose a resolution of d’Alembert’s Paradox comparing observation of substantial drag/lift in fluids with very small viscosity such as air and water, with the mathematical prediction of zero drag/lift of stationary irrotational solutions of the incompressible inviscid Euler equations, referred to as potential flow. We present analytical and computational evidence that (i) potential flow cannot be observed because it is illposed or unstable to perturbations, (ii) computed viscosity solutions of the Euler equations with slip boundary conditions initiated as potential flow, develop into turbulent solutions which are wellposed with respect to drag/lift and which show substantial drag/lift, in accordance with observations.

Mathematics Subject Classification (2000).

65M60 76E99 


D’Alembert’s Paradox Euler equations inviscid flow General Galerkin method illposed wellposed separation blowup 

Copyright information

© Birkhäuser Verlag, Basel 2008

Authors and Affiliations

  • Johan Hoffman
    • 1
  • Claes Johnson
    • 1
  1. 1.Computer Science and Communication, KTHStockholmSweden

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