In the framework of the Global Regularity Problem for the Navier-Stokes (NS) Equations in R3 Li and Sinai proved the existence of singular complex solutions (“blow-up”). We give an outline of their approach and discuss the perspectives of its extension to real solutions. We also illustrate, with the help of computer simulations, the behavior of a real solution related to the complex blow-up. It does not blow up, due to its approximate axial symmetry, but it shows a remarkable tornado-like behavior, with a rapid concentration and increase of speed and vorticity.
Boldrighini, C., Frigio, S., Maponi, P., Pellegrinotti, A., Sinai, Y.G. (2020). 3D incompressible Navier-Stockes equations: Complex blow up and related real flow. In Proceeding of Erevan conference 2019. Potsdam : Institut für Mathematik der Universität Potsdam.
3D incompressible Navier-Stockes equations: Complex blow up and related real flow
S. Frigio;A. Pellegrinotti;
2020-01-01
Abstract
In the framework of the Global Regularity Problem for the Navier-Stokes (NS) Equations in R3 Li and Sinai proved the existence of singular complex solutions (“blow-up”). We give an outline of their approach and discuss the perspectives of its extension to real solutions. We also illustrate, with the help of computer simulations, the behavior of a real solution related to the complex blow-up. It does not blow up, due to its approximate axial symmetry, but it shows a remarkable tornado-like behavior, with a rapid concentration and increase of speed and vorticity.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
