Copyright © 2011 Paula Curt and Denisa Fericean. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We study the time evolution of the free boundary of a viscous fluid for planar flows in Hele-Shaw cells under injection. Applying methods from the theory of univalent functions, we prove the invariance
in time of -likeness property (a geometric property which includes starlikeness
and spiral-likeness) for two basic cases: the inner problem and the
outer problem. We study both zero and nonzero surface tension models.
Certain particular cases are also presented.