Hele-Shaw moving boundary value problem in a bounded domain. Local in time solvability
Sergei Rogosin · Complex Variables Theory and Application An International Journal · 2005
In this article, a complex model for the Hele-Shaw flow in a bounded cell (mold) is studied. We introduce weighted spaces of analytic functions with piece-wise continuous boundary functions. On their base the scale of Banach spaces is constructed. The local (in time) solvability is obtained by reduction of a set of governing equations to an abstract Cauchy–Kovalevsky problem and by applying the Nirenberg–Nishida theorem in the constructed scale.