Resumen de Blow ups of complex solutions of the 3D Navier�Stokes system and renormalization group method

Dong Li, Yakov G. Sinai

• 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.

  Keywords: Navier-Stokes system, renormalization group theory, fixed point, linearization near the fixed point, spectrum of the linearized group, Hermite polynomials