SURFACE SINGULARITIES OF IDEAL FLUID

We show that the equations of motion of an ideal fluid with a free sur face due to inertial forces only can be effectively solved in the appr oximation of small surface angles. For almost arbitrary initial condit ions the system evolves to the formation of singularities in a finite time. Three kinds of singularities are shown to be possible: the root ones for which the process of the singularity formation represents som e analog of the wave breaking; singularities in the form of wedges on the interface; the floating ones associated with motion in the complex plane of the singular points of the analytical continuation of the su rface shape.