Hele-Shaw Flows: Historical Overview

Integrable Systems (2000–2007)
The Polubarinova-Galin equation written from the Poisson
bracket viewpoint as
Im
∂f
∂t
∂f
∂θ
= ∂(u,v)
∂(θ,t)
becomes the string constrain.
= ∂u
∂θ
∂v
∂t
− ∂v
∂θ
∂u
∂t
= Q
2π ,
Solutions lead to a reconstruction of the domain by its
moments.
• Wiegmann, Zabrodin: Random matrices.
• A.V.: Hele-Shaw worldsheet.
BIRS, Canada, July 2007 – p. 85