Domain of convergence of perturbative solutions for Hele-Shaw flow near interface collapse
نویسندگان
چکیده
Recent work @Phys. Fluids 10, 2701 ~1998!# 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 e 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 e. That length scale defines a ball in space and time, centered around the incipient singularity, inside of which perturbation theory fails. Implications of these results for a possible matching of outer solutions to inner scaling solutions are discussed. © 1999 American Institute of Physics. @S1070-6631~99!00910-1#
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