Some examples of singular fluid flows

2001/09/06 by Marco Romito, M. Romito, Romito, M.
Engineering · Mathematics · Physics and Astronomy · #35A20 #76D05 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics and Turbulent Flows #Lattice Boltzmann Simulation Studies #Mathematical Physics (math-ph) #Navier-Stokes equation solutions #math-ph #math.AP #math.MP #msc:35A20 #msc:76D05

paper · pdf · doi:10.48550/arxiv.math/0109040

14 pages, 1 figure

arxiv created 2001/09/06 · openalex publication_date 2001/09/06 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We explain the construction of some solutions of the Stokes system with a given set of singular points, in the sense of Caffarelli, Kohn and Nirenberg. By means of a partial regularity theorem (proved elsewhere), it turns out that we are able to show the existence of a suitable weak solution to the Navier-Stokes equations with a singular set of positive one dimensional Hausdorff measure.

Citations

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

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