Abstract: In the framework of the Global Regularity Problem for the incompressible Navier–Stokes (NS) equations in the whole space ℝ3, Li and Sinai in  proved that there are smooth complex solutions that become singular (“blow-up”). We discuss the possible extension of the Li-Sinai approach to real solutions and report results obtained by computer simulations on the behavior of a particular solution related to the complex blow-up. Although a blow-up is excluded by axial symmetry, the solution is a good model of a “tornado-like” behavior, with a sharp increase of speed and vorticity concentrated in an annular region around the symmetry axis. We conclude with a discussion on the search of possible candidates for a real blow-up in the framework of the Li-Sinai approach.
All Science Journal Classification (ASJC) codes
- Physics and Astronomy(all)