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Physics of Fluids
Recent work ͓Phys. Fluids 10, 2701 ͑1998͔͒ has shown that for Hele-Shaw flows sufficiently near a finite-time pinching singularity, there is a breakdown of the leading-order solutions perturbative in a small parameter ⑀ controlling the large-scale dynamics. To elucidate the nature of this breakdown we study the structure of these solutions at higher order. We find a finite radius of convergence that yields a new length scale exponentially small in ⑀. That length scale defines a ball in spacedoi:10.1063/1.870139 fatcat:5p6jwpxxzbfodajzetcgimfjjy