Hele-Shaw Flows: Historical Overview

Free Boundary Problem
• ∆p = Qδ0(z), for z ∈ Ω(t);
•
p = 0, where Γ(t) = ∂Ω(t);
• ∂p
∂n
z∈Γ(t)
z∈Γ(t)
= −v n .
Q < 0 for injection, Q > 0 for sucction.
In the case of surface tension replace 0 by βκ(z,t) where
β is surface tension, κ is the mean curvature.
BIRS, Canada, July 2007 – p. 37