Convexity of the free boundary for an axially symmetric rotational cavity flow problem

Abstract

In Friedman’s work [Commun. Partial Differ. Equations 8, 949−997 (1983)], the existence and uniqueness of axially symmetric incompressible rotational cavity flow were established. Based on his work, we establish the convexity of the free boundary for the axially symmetric rotational cavity flows. As by-products, we also give the asymptotic behavior in the far-field.