On the blow-up of some complex solutions of the 3-d Navier-Stokes\n Equations: Theoretical Predictions and Computer simulations

2017/02/23 by C. Boldrighini, Boldrighini, Carlo, S. Frigio +3
Engineering · Mathematics · #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics and Turbulent Flows #Lattice Boltzmann Simulation Studies #Mathematical Physics (math-ph) #Navier-Stokes equation solutions #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1702.07139

openalex publication_date 2017/02/23 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28

Abstract

We consider some complex-valued solutions of the Navier-Stokes equations in\nR³ for which Li and Sinai proved a finite time blow-up. We show that there\nare two types of solutions, with different divergence rates, and report results\nof computer simulations, which give a detailed picture of the blow-up for both\ntypes. They reveal in particular important features not, as yet, predicted by\nthe theory, such as a concentration of the energy and the enstrophy around a\nfew singular points, while elsewhere the "fluid" remains quiet.\n

Citations

• Sur le mouvement d'un liquide visqueux emplissant l'espace

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