Computer simulations for the blow-up of complex solutions of the 3-d Navier-Stokes equations
Provides numerical evidence for blow-up in a class of Navier-Stokes solutions, relevant to understanding singularity formation in fluid dynamics.
The paper uses computer simulations to study complex-valued solutions of the 3D Navier-Stokes equations that exhibit finite-time blow-up, revealing energy and enstrophy concentration in small regions.
We present a study by computer simulations of a class of complex-valued solutions of the three-dimensional Navier-Stokes equations in the whole space, which, according to Li and Sinai, present a blow-up (singularity) at a finite time. The computer results allow a detailed study of the blow-up mechanism, and show interesting features of the behavior of the solutions near the blow-up time, such as the concentration of energy and enstrophy in a small region around a few points of physical space, while outside this region the "fluid" remains "quiet".