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On Liouville type theorem for the stationary Navier–Stokes equations.
- Source :
- Calculus of Variations & Partial Differential Equations; Jun2019, Vol. 58 Issue 3, pN.PAG-N.PAG, 1p
- Publication Year :
- 2019
-
Abstract
- In this paper we prove a Liouville type theorem for the stationary Navier–Stokes equations in R 3 . Let V = (V ij) be a potential function of a smooth solution u, which means u = ∇ · V . We show that if there exists 3 < s < + ∞ such that the L s mean oscillation of the potential function has certain growth condition near infinity, namely 1 | B (r) | ∫ B (r) | V - V B (r) | s d x ≤ C r min { s - 3 3 , s 6 } ∀ 1 < r < + ∞ , then u ≡ 0 . [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 09442669
- Volume :
- 58
- Issue :
- 3
- Database :
- Complementary Index
- Journal :
- Calculus of Variations & Partial Differential Equations
- Publication Type :
- Academic Journal
- Accession number :
- 137077454
- Full Text :
- https://doi.org/10.1007/s00526-019-1549-5