Weak Singularity for Two-Dimensional Nonlinear Equations of   Hydrodynamics and Propagation of Shock Waves
  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. 
Vitaly V. Bulatov (Institute for Problems in Mechanics, Russia), Yuriy   V. Vladimirov (Institute for Problems in Mechanics,...