Desingularization of Vortices for the Euler Equation

By D. Smets, Jean Van Schaftingen. 2009

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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.

Subfields: Applied Mathematics, Control and Systems Engineering, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/88009c57946f1806e379e77d0afb1b7e3804f6f0