Archive for Rational Mechanics and Analysis

, Volume 204, Issue 2, pp 479–513 | Cite as

Harmonic Maps and Ideal Fluid Flows

  • A. Aleman
  • A. ConstantinEmail author


Using harmonic maps we provide an approach towards obtaining explicit solutions to the incompressible two-dimensional Euler equations. More precisely, the problem of finding all solutions which in Lagrangian variables (describing the particle paths of the flow) present a labelling by harmonic functions is reduced to solving an explicit nonlinear differential system in \({\mathbb {C^n}}\) with n = 3 or n = 4. While the general solution is not available in explicit form, structural properties of the system permit us to identify several families of explicit solutions.


Vorticity Euler Equation Explicit Solution Water Wave Connected Domain 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Matematik NFLund UniversityLundSweden
  2. 2.Faculty of MathematicsUniversity of ViennaViennaAustria

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