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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. (Publisher's Version)
In: Advances in Nonlinear Analysis, 10 (1), pp. 1071-1085. De Gruyter, ISSN 2191-9496,
DOI: 10.26083/tuprints-00019237,
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Item Type: Article
Origin: Secondary publication via sponsored Golden Open Access
Status: Publisher's Version
Title: Optimality of Serrin type extension criteria to the Navier-Stokes equations
Language: English
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.

Journal or Publication Title: Advances in Nonlinear Analysis
Journal volume: 10
Number: 1
Publisher: De Gruyter
Classification DDC: 500 Naturwissenschaften und Mathematik > 510 Mathematik
Divisions: 04 Department of Mathematics > Analysis
Date Deposited: 30 Jul 2021 08:07
Last Modified: 30 Jul 2021 08:07
DOI: 10.26083/tuprints-00019237
Corresponding Links:
URN: urn:nbn:de:tuda-tuprints-192377
URI: https://tuprints.ulb.tu-darmstadt.de/id/eprint/19237
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