  A system of two-dimensional nonlinear equations of hydrodynamics is
considered. It is shown that for the this system in the general case a solution
with weak discontinuity-type singularity behaves as a square root of S(x,y,t),
where S(x,y,t)>0 is a smooth function. The necessary conditions and series of
corresponding differential equations are obtained for the existence of a
solution.
