Complex singularities of solutions of some 1D hydrodynamic models

We study the complex singularities of solutions of some classes of 1D hydrodynamic models. The method is based on the renormalization group theory. We derive the equation for the corresponding fixed point and study the spectrum of the linearized map near this point. This information allows to describe the initial condition for which blow ups at finite time can occur. We should stress that our solutions having blow ups are complex-valued.