Desingularization of vortices for the Euler equation

Details Desingularization of vortices for the Euler equation Desingularization of vortices for the Euler equation

2009-09-07

arxiv.org/abs/0909.1166v2

Arch. Rat. Mech. Anal. 198 (2010), no. 3, 869-925

Mathematics

Analysis of PDEs

40 pages

Scientific paper

10.1007/s00205-010-0293-y

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.

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