Singularity & Regularity Issues for Simplified Models of Turbulence

2011/03/03 by Hani Ali, Ali, Hani, Zied Ammari +1
Economics, Econometrics and Finance · Engineering · Mathematics · #35Q30 #35Q35 #76F60 #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations #Stochastic processes and financial applications #math.AP #msc:35Q30 #msc:35Q35 #msc:76F60

paper · pdf · doi:10.48550/arxiv.1103.0796

arxiv created 2011/03/03 · openalex publication_date 2011/03/03 · arxiv updated 2011/03/07 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We consider a family of Leray-α models with periodic boundary conditions in three space dimensions. Such models are a regularization, with respect to a parameter θ, of the Navier-Stokes equations. In particular, they share with the original equation (NS) the property of existence of global weak solutions. We establish an upper bound on the Hausdorff dimension of the time singular set of those weak solutions when θ is subcritical. The result is an interpolation between the bound proved by Scheffer for the Navier-Stokes equations and the regularity result proved in \citeA01.

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