| Abstract: | An extension of the method of moments proposed by Richardson to Hele-Shaw flows with a free boundary generated by multipoles is considered. The evolution of the circular contour is investigated in relation to the operation of a single multipole of ordern at the zero or at an infinitely remote point. It is shown that a solution exists only up to a certain momentt*, when on the boundary of the domainn symmetric cusps directed towards the multipole are formed. For an arbitrary initial domain it is possible to obtain an estimate of the period of existence of a solution.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 121–127, September–October, 1993. |
