Archive for Rational Mechanics and Analysis

, Volume 198, Issue 3, pp 869–925 | Cite as

Desingularization of Vortices for the Euler Equation

  • Didier SmetsEmail author
  • Jean Van Schaftingen


We study the existence of stationary classical solutions of the incompressible Euler equation in the planes that approximate singular stationary solutions of this equation. The construction is performed by studying the asymptotics of equation \({-\varepsilon^2 \Delta u^\varepsilon=(u^\varepsilon-q-\frac{\kappa}{2\pi} \log \frac{1}{\varepsilon})_+^p}\) with Dirichlet boundary conditions and q a given function. We also study the desingularization of pairs of vortices by minimal energy nodal solutions and the desingularization of rotating vortices.


Vortex Vorticity Euler Equation Vortex Ring Vortex Pair 
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Authors and Affiliations

  1. 1.Laboratoire Jacques-Louis LionsUniversité Pierre et Marie CurieParisFrance
  2. 2.Départment de MathématiqueUniversité catholique de LouvainLouvain-la-NeuveBelgium

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