Viscous flow at infinite marangoni number

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