Non-trivial self-similar extinction solutions for a 3D Hele-Shaw suction problem
نویسندگان
چکیده
We show the existence of noncircular, self-similar solutions to the three-dimensional Hele-Shaw suction problem with surface tension regularisation up to complete extinction. In an appropriate scaling, these solutions are found as bifurcation solutions to a nonlocal elliptic equation of order three. The bifurcation parameter is the ratio of the suction speed and the surface tension coefficient. AMS subject classification: 35R35, 76D27, 47J15
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