Singularities in Hele-Shaw flows driven by a multipole (Q2783715)

The authors study, from analytical and numerical points of view, the singularity formation in an interface flow driven by a multipole in two-dimensional Hele-Shaw cell with surface tension. They prove that the singularity formation is inevitable in the case of a dipole. Also for a multipole of higher order, they show that the solution will develop finite time singularities. From numerical studies it follows that the solution develops finite time singularities via an interface reaching the multipole while forming a corner at the tip of the finger that touches the multipole. The authors also estimate the distance between the finger tip and multipole as a function of time. The theoretical results are in good agreement with numerical computations.