A Verigin problem with kinetic condition (Q1369471)

This paper deals with a free boundary problem describing the motion of two immiscible fluids: oil and water. The classical pressure continuity on the free boundary is replaced with a more general condition \(p_1- p_2= ak+ bV\), where \(p_1\) and \(p_2\) are the pressures of the two fluids, \(k\) is the mean curvature of the free boundary, \(V\) is normal velocity of the free boundary, and \(a\), \(b\) are nonnegative constants. The author obtains existence and uniqueness of classical solution locally in time for \(a= 0\).