Complex Singular Solutions of the 3-d Navier–Stokes Equations and Related Real Solutions

By applying methods of statistical physics Li and Sinai (J Eur Math Soc 10:267–313, 2008 ) proved that there are complex solutions of the Navier–Stokes equations in the whole space R 3 which blow up at a finite time. We present a review of the results obtained so far, by theoretical work and computer simulations, for the singular complex solutions, and compare with the behavior of related real solutions. We also discuss the possible application of the techniques introduced in (J Eur Math Soc 10:267–313, 2008 ) to the study of the real ones.