Blow ups of complex solutions of the 3D Navier–Stokes system and renormalization group method

Abstract

We consider complex-valued solutions of the three-dimensional Navier-Stokes system without external forcing on $R^3$. We show that there exists an open set in the space of $10$-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.