VISCOUS-FLOW AT INFINITE MARANGONI NUMBER

We formulate the theory of surface tension driven Stokes flow set up b y an active scalar with zero diffusivity. The 3D hydrodynamic problem can be reduced to a 2D nonlinear evolution equation involving only fre e surface quantities. For a semi-infinite layer it can be rigorously d emonstrated that the solutions to this equation blow up in finite time and develop singular forms. The new type of nonlinearity plays a univ ersal role in the description of interfacial turbulence.