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Vortices and localization in Euler flows. (English) Zbl 0774.35058
Summary: We study the time evolution of a nonviscous incompressible two- dimensional fluid when the initial vorticity is concentrated in \(N\) small disjoint regions of diameter \(\varepsilon\). We prove that the time evolved vorticity is also concentrated in \(N\) regions of diameter \(d\), vanishing as \(\varepsilon\to 0\). As a consequence we give a rigorous proof of the validity of the point vortex system. The same problem is examined in the context of the vortex-wave system.

MSC:
35Q35 PDEs in connection with fluid mechanics
76B47 Vortex flows for incompressible inviscid fluids
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