Complex Singularities of the Burgers System and Renormalization Group Method

Abstract

We consider complex-valued solutions of the n-dimensional Burgers' system, $n \gt 1$. We show that there exists an open set in the space of $n^2 + 5n - 2/2$-parameter families of initial conditions such that for each family from this set there are values of parameters for which the solution develops blow up in finite time.