Serfati, Philippe A direct proof of global existence of \(2D\) vortex patches. (Une preuve directe d’existence globale des vortex patches \(2D\).) (French) Zbl 0803.76022 C. R. Acad. Sci., Paris, Sér. I 318, No. 6, 515-518 (1994). 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 Cited in 30 Documents MSC: 76B47 Vortex flows for incompressible inviscid fluids 35Q35 PDEs in connection with fluid mechanics Keywords:regularity; two-dimensional incompressible Euler equation; regular curve PDFBibTeX XMLCite \textit{P. Serfati}, C. R. Acad. Sci., Paris, Sér. I 318, No. 6, 515--518 (1994; Zbl 0803.76022)