Global vortex sheet solutions of Euler equations in the plane (Q1117404)

This paper deals with the singular solutions of the Euler equations for an incompressible perfect fluid in the plane. The authors employ a fixed-point technique in order to prove that if the initial vorticity density \(\Omega_ 0\) is not arbitrary but is chosen depending on the initial sheet \(\Gamma_ 0\), the vortex sheet \(\Gamma_ t\) exists for all \(t>0.\) In addition, \(\Gamma_ t\) and \(\Omega\) (t) (the vorticity density at \(t>0)\) become analytic for \(t>0\) and they converge to a straight line and to a constant, respectively, for infinite t.