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.
1
Universidad Técnica Federico Santa María, Valparaíso, Chile
2
University of Bergen, Norway
Alexander Vasil'ev; Irina Markina. On the geometry of Hele-Shaw flows with small surface tension. Interfaces and free boundaries, Tome 5 (2003) no. 2, pp. 183-192. doi: 10.4171/ifb/77
@article{10_4171_ifb_77,
author = {Alexander Vasil'ev and Irina Markina},
title = {On the geometry of {Hele-Shaw} flows with small surface tension},
journal = {Interfaces and free boundaries},
pages = {183--192},
year = {2003},
volume = {5},
number = {2},
doi = {10.4171/ifb/77},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/77/}
}
TY - JOUR
AU - Alexander Vasil'ev
AU - Irina Markina
TI - On the geometry of Hele-Shaw flows with small surface tension
JO - Interfaces and free boundaries
PY - 2003
SP - 183
EP - 192
VL - 5
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.4171/ifb/77/
DO - 10.4171/ifb/77
ID - 10_4171_ifb_77
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%T On the geometry of Hele-Shaw flows with small surface tension
%J Interfaces and free boundaries
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%N 2
%U http://geodesic.mathdoc.fr/articles/10.4171/ifb/77/
%R 10.4171/ifb/77
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