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Applicable Analysis
An International Journal
Volume 101, 2022 - Issue 16
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Research Article

A regularity criterion for 3D NSE in ‘dynamically restricted’ local Morrey spaces

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Pages 5809-5823 | Received 08 Jan 2021, Accepted 11 Mar 2021, Published online: 29 Mar 2021
 

ABSTRACT

It is shown that a local-in-time strong solution u to the 3D Navier–Stokes equations remains regular on an interval (0,T) provided a smallness ϵ0-condition on u in a dynamically restricted local Morrey space is stipulated; more precisely, supt(0,T)supxR3,η(t)r11rαBr(x)|u(y,t)|pdyϵ0,where η is a dynamic dissipation scale consistent with the turbulence phenomenology and α and p are suitable parameters. Such regularity criterion guarantees the volumetric sparseness of local spatial structure of intense vorticity components, preventing the formation of the finite-time blow up at T under the framework of Zα-sparseness classes introduced in Bradshaw et al. (An algebraic reduction of the ‘Scaling Gap’ in the Navier–Stokes regularity problem. Arch Ration Mech Anal. 2019;231(3):1983–2005).

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Disclosure statement

No potential conflict of interest was reported by the author(s).

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