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Regularity criterion for weak solutions to the Navier–Stokes equations in terms of the pressure in the class

✍ Scribed by Xiaowei He; Sadek Gala

Book ID
113823950
Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
213 KB
Volume
12
Category
Article
ISSN
1468-1218

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## Abstract Consider the nonstationary Navier–Stokes equations in Ω × (0, __T__), where Ω is a bounded domain in ℝ^3^. We prove interior regularity for suitable weak solutions under some condition on the pressure in the class of scaling invariance. The notion of suitable weak solutions makes it pos

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In this note we establish a Serrin-type regularity criterion in terms of pressure for Leray weak solutions to the Navier-Stokes equation in R d . Here we call u a Leray weak solution if u is a weak solution of finite energy, i.e. It is known that if a Leray weak solution u belongs to then u is reg