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Desingularization of vortices for the Euler equation. (English) Zbl 1228.35171
The authors study the existence of stationary solutions for the Euler equations of inviscid incompressible flows in two dimensions, which approximate singular solutions (vortices) of the same problem. The method they use consists in studying the asymptotics of the semi-linear elliptic equation
\[ -\varepsilon^2 \Delta u^{\varepsilon}=\left(u^{\varepsilon}-q-\frac{\kappa}{2\pi}\;\log\frac{1}{\varepsilon}\right)^p_+, \] with Dirichlet boundary conditions, for a given function \(q\) and a positive \(\kappa\), when \(\varepsilon\rightarrow 0\).

MSC:
35Q31 Euler equations
76B47 Vortex flows for incompressible inviscid fluids
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