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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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##### References:
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