CLASSICAL SOLVABILITY OF THE RADIAL VISCOUS FINGERING PROBLEM IN A HELE-SHAW CELL WITH SURFACE TENSION

摘要

We consider the one-phase problem on radial viscous fingering structures in a Hele-Shaw cell with surface tension. This problem is a nonlinear free-boundary problem for elliptic equations. Unlike the Stefan problem for the heat equation, we deal with a problem of hydrodynamic type. We establish the classical solvability of the one-phase Hele-Shaw problem with radial geometry by using the same method as that used for the Stefan problem and justifying the vanishing coefficient of the time-derivative in the parabolic equation. Bibliography: 15 titles.