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

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Shvydkoy, Roman Leslie, Trevor M.
Copyright Year	2018
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 $L^4 L^4$ result in the case $d<1$. Additionally, we establish energy equality in certain cases of Type-I blow up. The results are also extended to the NSE with fractional power of the Laplacian below $1$.
Sponsorship	National Science Foundation
Starting Page	870
Ending Page	890
Page Count	21
File Format	PDF
ISSN	00361410
DOI	10.1137/16M1104147
e-ISSN	10957154
Journal	SIAM Journal on Mathematical Analysis (SJMAAH)
Issue Number	1
Volume Number	50
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2018-02-06
Access Restriction	Subscribed
Subject Keyword	Onsager conjecture PDEs in connection with fluid mechanics energy equality Flows in porous media; filtration; seepage Navier--Stokes
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Analysis Computational Mathematics

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