General solution of the one-phase Hele-Shaw problem for elliptic bubble
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 152 (2010) no. 1, pp. 80-92
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In the general case of several multipole we study one-phase Hele-Shaw flow with a moving boundary when surface tension effect is negligible. We find the explicit solution with nonstationary elliptic shape of the bubble for case when Hele-Shaw flow is produced by any combination of sink, dipole and quadropole at infinity. This general solution includes all known particular cases. In the particular case of a dipole at infinity we find new explicit solution with stationary elliptic shape of the bubble that is not symmetrical with respect to the flow.
Keywords:
one-phase Hele-Shaw problem, elliptic bubble.
@article{UZKU_2010_152_1_a7,
author = {M. M. Alimov},
title = {General solution of the one-phase {Hele-Shaw} problem for elliptic bubble},
journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
pages = {80--92},
publisher = {mathdoc},
volume = {152},
number = {1},
year = {2010},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/UZKU_2010_152_1_a7/}
}
TY - JOUR AU - M. M. Alimov TI - General solution of the one-phase Hele-Shaw problem for elliptic bubble JO - Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki PY - 2010 SP - 80 EP - 92 VL - 152 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/UZKU_2010_152_1_a7/ LA - ru ID - UZKU_2010_152_1_a7 ER -
%0 Journal Article %A M. M. Alimov %T General solution of the one-phase Hele-Shaw problem for elliptic bubble %J Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki %D 2010 %P 80-92 %V 152 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/UZKU_2010_152_1_a7/ %G ru %F UZKU_2010_152_1_a7
M. M. Alimov. General solution of the one-phase Hele-Shaw problem for elliptic bubble. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 152 (2010) no. 1, pp. 80-92. http://geodesic.mathdoc.fr/item/UZKU_2010_152_1_a7/