Asymptotic stability for the Navier-Stokes equations

Jishan Fan; Tohru Ozawa

doi:10.1007/s00028-008-0396-1

Asymptotic stability for the Navier-Stokes equations

Jishan Fan, Tohru Ozawa

Research output: Contribution to journal › Article

2 Citations (Scopus)

Abstract

We prove the asymptotic stability for weak solutions to the 3-D Navier-Stokes equations in the class ∇u ∈ L¹(0, ∞; Ḃ_∞∞⁰(ℝ³)) ∩ LLogL(0, ∞; Ḃ_∞∞⁰(ℝ³)) with arbitrary initial and external perturbations. This solves a problem due to Yong Zhou (Proc. Roy. Soc. Edinburgh, 136A (2006), 1099-1109).

Original language	English
Pages (from-to)	379-389
Number of pages	11
Journal	Journal of Evolution Equations
Volume	8
Issue number	2
DOIs	https://doi.org/10.1007/s00028-008-0396-1
Publication status	Published - 2008 May 1
Externally published	Yes

Keywords

Asymptotic stability
Besov spaces
Navier-Stokes equations

ASJC Scopus subject areas

Mathematics (miscellaneous)

Access to Document

10.1007/s00028-008-0396-1

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Cite this

Fan, J., & Ozawa, T. (2008). Asymptotic stability for the Navier-Stokes equations. Journal of Evolution Equations, 8(2), 379-389. https://doi.org/10.1007/s00028-008-0396-1

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AB - We prove the asymptotic stability for weak solutions to the 3-D Navier-Stokes equations in the class ∇u ∈ L1(0, ∞; Ḃ∞∞0(ℝ3)) ∩ LLogL(0, ∞; Ḃ∞∞0(ℝ3)) with arbitrary initial and external perturbations. This solves a problem due to Yong Zhou (Proc. Roy. Soc. Edinburgh, 136A (2006), 1099-1109).

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