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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
Article

Abstract

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.

Keywords

Vortex Vorticity Euler Equation Vortex Ring Vortex Pair 
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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Copyright information

© Springer-Verlag 2010

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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