Farwig, Reinhard ; Kanamaru, Ryo (2020)
Optimality of Serrin type extension criteria to the Navier-Stokes equations.
In: Advances in Nonlinear Analysis, 10 (1)
doi: 10.1515/anona-2020-0130
Article, Bibliographie
This is the latest version of this item.
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: | 2020 |
| Creators: | Farwig, Reinhard ; Kanamaru, Ryo |
| Type of entry: | Bibliographie |
| Title: | Optimality of Serrin type extension criteria to the Navier-Stokes equations |
| Language: | English |
| Date: | 2020 |
| Publisher: | De Gruyter |
| Journal or Publication Title: | Advances in Nonlinear Analysis |
| Volume of the journal: | 10 |
| Issue Number: | 1 |
| DOI: | 10.1515/anona-2020-0130 |
| Corresponding Links: | |
| 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. |
| Classification DDC: | 500 Science and mathematics > 510 Mathematics |
| Divisions: | 04 Department of Mathematics 04 Department of Mathematics > Analysis |
| Date Deposited: | 02 Aug 2024 12:35 |
| Last Modified: | 02 Aug 2024 12:35 |
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| Suche nach Titel in: | TUfind oder in Google |
Available Versions of this Item
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Optimality of Serrin type extension criteria to the Navier-Stokes equations. (deposited 30 Jul 2021 08:07)
- Optimality of Serrin type extension criteria to the Navier-Stokes equations. (deposited 02 Aug 2024 12:35) [Currently Displayed]
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