We consider complex-valued solutions of the three-dimensional Navier-Stokes system without external forcing on . We show that there exists an open set in the space of -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.
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Dong Li, Yakov G. Sinai, Blow ups of complex solutions of the 3D Navier–Stokes system and renormalization group method. J. Eur. Math. Soc. 10 (2008), no. 2, pp. 267–313DOI 10.4171/JEMS/111