We start with the Cauchy problem for the multidimensional Burgers type equation with periodic boundary conditions. We introduce the notion of degeneracy for vector fields. Vector field $u$ is degenerate iff one of the following equivalent conditions holds: (*) the Jacoby matrix of $u$ is everywhere nilpotent (*) the pressureless Euler equation with the initial state $u$ is globally solvable in the class of $C1$-continuous functions. Non-degenerate initial states develops large spatial derivatives (turbulence). In 2D there is a nice geometric criterion for degeneracy due to Pogorelov cylinder theorem.