Didier Smets, Jean Van Schaftingen
Published 2009-09-07, updated 2009-10-12Version 2
We study the existence of stationary classical solutions of the incompressible Euler equation in the plane that approximate singular stationnary solutions of this equation. The construction is performed by studying the asymptotics of equation $-\eps^2 \Delta u^\eps=(u^\eps-q-\frac{\kappa}{2\pi} \log \frac{1}{\eps})_+^p$ 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.
Comments: 40 pages
Journal: Arch. Rat. Mech. Anal. 198 (2010), no. 3, 869-925
Desingularization of vortices for the incompressible Euler equation on a sphere
On the pure critical exponent problem for the $p$-Laplacian
On the torsion function with Robin or Dirichlet boundary conditions
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