  We consider the motion of the interface separating two domains of the same
fluid that moves with different velocity along the tangential direction of the
interface. We assume that the fluids occupying the two domains are of constant
densities that are equal, are inviscid, incompressible and irrotational, and
that the surface tension is zero. We discuss results on the existence and
uniqueness of solutions for given data, the regularity of solutions,
singularity formation and the nature of solutions after the singularity
formation time.

Analysis of PDEs