Hele-Shaw Flows: Historical Overview
Hele-Shaw Flows: Historical Overview
Hele-Shaw Flows: Historical Overview
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Fingering and ill-posed problems<br />
• Receding viscous fluid performs an ill-posed problem.<br />
• Kinetic undercooling regularization (Reissig, Hohlov,<br />
Rogozin, Entov from 1995)<br />
β ∂p<br />
∂n<br />
+ p = 0, on Γ(t), β > 0.<br />
• Surface tension regularization<br />
<br />
<br />
p = βκ(z,t).<br />
z∈Γ(t)<br />
BIRS, Canada, July 2007 – p. 63