The flow of elastically superstarlike domains in Hele-Shaw cells

Abstract We introduce a geometric property built upon two geometric conditions that have been shown to be invariant (in certain cases) for the Hele-Shaw flow problem, in recent results by the same author (Aron in J Math Fluid Mech, Aron in Time evolution of elastically starlike domains in the Hele-Shaw flow problem, to appear). The new property is analytically characterized, and its invariance under the Hele-Shaw evolution is investigated. The results obtained show that the property of $$\sigma $$ σ -superstarlikeness of the initial fluid domain, together with lower and upper bounds on the elasticity on the boundary, are preserved under the time evolution for suitable choices of these bounds and of the parameter $$\sigma >0$$ σ > 0 , in the case of the interior version of the Hele-Shaw flow problem. In particular, our results recover and refine several invariance results previously obtained by other authors.