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Optimality of Serrin type extension criteria to the Navier-Stokes equations

Farwig, Reinhard ; Kanamaru, Ryo (2021)
Optimality of Serrin type extension criteria to the Navier-Stokes equations.
In: Advances in Nonlinear Analysis, 2020, 10 (1)
doi: 10.26083/tuprints-00019237
Article, Secondary publication, Publisher's Version

Abstract

We prove that a strong solution u to the Navier-Stokes equations on (0, T) can be extended if either u ∈ L θ (0, T; U˙ −α ∞,1/θ,∞) for 2/θ + α = 1, 0 < α < 1 or u ∈ L 2 (0, T; V˙ 0 ∞,∞,2 ) , where U˙ s p,β,σ and V˙ s p,q,θ are Banach spaces that may be larger than the homogeneous Besov space B˙ s p,q. Our method is based on a bilinear estimate and a logarithmic interpolation inequality.

Item Type: Article
Erschienen: 2021
Creators: Farwig, Reinhard ; Kanamaru, Ryo
Type of entry: Secondary publication
Title: Optimality of Serrin type extension criteria to the Navier-Stokes equations
Language: English
Date: 2021
Year of primary publication: 2020
Publisher: De Gruyter
Journal or Publication Title: Advances in Nonlinear Analysis
Volume of the journal: 10
Issue Number: 1
DOI: 10.26083/tuprints-00019237
URL / URN: https://tuprints.ulb.tu-darmstadt.de/19237
Corresponding Links:
Origin: Secondary publication via sponsored Golden Open Access
Abstract:

We prove that a strong solution u to the Navier-Stokes equations on (0, T) can be extended if either u ∈ L θ (0, T; U˙ −α ∞,1/θ,∞) for 2/θ + α = 1, 0 < α < 1 or u ∈ L 2 (0, T; V˙ 0 ∞,∞,2 ) , where U˙ s p,β,σ and V˙ s p,q,θ are Banach spaces that may be larger than the homogeneous Besov space B˙ s p,q. Our method is based on a bilinear estimate and a logarithmic interpolation inequality.

Status: Publisher's Version
URN: urn:nbn:de:tuda-tuprints-192377
Classification DDC: 500 Science and mathematics > 510 Mathematics
Divisions: 04 Department of Mathematics
04 Department of Mathematics > Analysis
Date Deposited: 30 Jul 2021 08:07
Last Modified: 03 Aug 2021 06:59
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