The evolution of a spatially periodic, perturbed vortex sheet following the formation of a curvature singularity at time t_c (Moore, D.W.,Proc. R. Soc. A, 1979) is discussed. First the Moore asymptotic solution is analyzed in terms of polylogarithmic functions to give the sheet shape at t=t_c, including phase information. This defines an intermediate, post-singularity evolution problem which is approximated as a time-wise Taylor-series expansion where coefficients are calculated by repeated differentiation of the defining Birkhoff-Rott (BR) equation. Next, the series is summed providing an analytic continuation which shows sheet rupture for t>tc but with some non-physical features. An inner solution is constructed based on a perturbed similarity formulation. Numerical solutions of both the inner, nonlinear zeroth-order and first-order linear BR equations are obtained whose outer limits match the intermediate solution. The composite solution shows a viable, but possibly not unique continuation of the vortex-sheet evolution beyond singularity formation. Properties of the intermediate and inner solutions are discussed.
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