Conditions Implying Energy Equality for Weak Solutions of the Navier--Stokes Equations

2016/06/08 by Leslie, Trevor M., Shvydkoy, Roman · 2 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1606.02363

Abstract

When a Leray--Hopf weak solution to the NSE has a singularity set S of dimension d less than 3---for example, a suitable weak solution---we find a family of new L^q L^p conditions that guarantee validity of the energy equality. Our conditions surpass the classical Lions--Ladyženskaja L⁴ L⁴ result in the case d<1. Additionally, we establish energy equality in certain cases of Type-I blowup. The results are also extended to the NSE with fractional power of the Laplacian below 1.

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