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A direct proof of global existence of \(2D\) vortex patches. (Une preuve directe d’existence globale des vortex patches \(2D\).) (French) Zbl 0803.76022

We give in detail an elementary and self-contained proof of the result: for all solution \(u(x,t)\) of the two-dimensional incompressible Euler equation, it exists a function \(\phi(x,t)\) such that, \(\forall t\geq 0\), \(u\) is regular (in \(x\)) on the regular level lines (in \(x\)) of \(\phi\), if this is true at \(t=0\) (an alternative case – with the same conclusion – is \(u\) being regular out of one regular curve).
Reviewer: P.Serfati

MSC:

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