On the Energy Equality for Distributional Solutions to Navier-Stokes\n Equations

2017/10/16 by Giovanni P. Galdi, Galdi, Giovanni P. · 3 citations
Engineering · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1710.05725

openalex publication_date 2017/10/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A classical result of J.-L. Lions asserts that if a solution to the\nNavier-Stokes equations is such that: (i) it is in the Leray-Hopf class, and\n(ii) belongs to L⁴(0,T;L⁴), then it must satisfy the energy equality in the\ntime interval [0,T]. In this note we show that assumption (i) is not\nnecessary.\n

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• On the weak solutions to the navier-Stokes equations: a possible gap related to the energy equality
• Quantitative classification of potential Navier-Stokes singularities beyond the blow-up time
• Energy equality of the weak solutions to the fractional Navier-Stokes / MHD equations

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