Desingularization of Vortices for the Euler Equation

@article{Smets2010DesingularizationOV,
  title={Desingularization of Vortices for the Euler Equation},
  author={Didier Smets and Jean Van Schaftingen},
  journal={Archive for Rational Mechanics and Analysis},
  year={2010},
  volume={198},
  pages={869-925}
}
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… 
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