On the Uniqueness of the Classical Solution of the Fingering Problem in a Hele-Shaw Cell with Surface Tension
A. Tani1, H. Tani2
1Keio University, Yokohama, Japan
2JANUS, Yokohama, Japan
Keywords: radial fingering structure, viscous fluid flow, Hele-Shaw cell, surface tension, unique classical solution
Abstract
The existence of a classical solution was established for a one-phase radial viscous fingering problem in a Hele-Shaw cell under surface tension (original problem) by means of parabolic regularization for a certain subsequence {εn}n∈N, εn > 0. In this paper, we prove the uniqueness of the classical solution to the original problem with the use of parabolic regularization for the full sequence of the parameter {ε}, ε > 0.
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