We consider some complex-valued solutions of the Navier–Stokes equations in R^3 for which Li and Sinai proved a finite time blow-up. We show that there are two types of solutions, with different divergence rates, and report results of computer simulations, which give a detailed picture of the blow-up for both types. They reveal in particular important features not, as yet, predicted by the theory, such as a concentration of the energy and the enstrophy around a few singular points, while elsewhere the ‘fluid’ remains quiet.
On the blow-up of some complex solutions of the 3D Navier–Stokes equations: theoretical predictions and computer simulations
Frigio, S.;Maponi, P.
2017-01-01
Abstract
We consider some complex-valued solutions of the Navier–Stokes equations in R^3 for which Li and Sinai proved a finite time blow-up. We show that there are two types of solutions, with different divergence rates, and report results of computer simulations, which give a detailed picture of the blow-up for both types. They reveal in particular important features not, as yet, predicted by the theory, such as a concentration of the energy and the enstrophy around a few singular points, while elsewhere the ‘fluid’ remains quiet.File in questo prodotto:
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IMA Journal of Applied Mathematics (2017) 82, 697–716.pdf
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Boldrighini, Frigio, Maponi pre-print.pdf
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Descrizione: arXiv:1702.07139v1 [math-ph] 23 Feb 2017
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