The Two-Phase Hele-Shaw Problem with a Nonregular Initial Interface and Without Surface Tension - Bazaliy, B.V.; Vasylyeva, N. (Журнал математической физики, анализа, геометрии, 2014)
In the paper, we consider the two-dimensional Muskat problem without surface tension on a free boundary. The initial shape of the unknown interface has a corner point. We prove that the problem has a unique solution in the weighted Hölder classes locally in time and specify the sufficient conditions for the existence of the "waiting time" phenomenon.