We study the time evolution of the free boundary of a viscous fluid in the non-zero-surface-tension models for planar flows in Hele-Shaw cells under injection. Applying methods of conformal map we prove that certain geometric properties, such as starlikeness and directional convexity, are preserved in time.
Cite this article
Alexander Vasil'ev, Irina Markina, On the geometry of Hele-Shaw flows with small surface tension. Interfaces Free Bound. 5 (2003), no. 2, pp. 183–192DOI 10.4171/IFB/77