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 › peer-review

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
Externally published	Yes

Keywords

Asymptotic stability
Besov spaces
Navier-Stokes equations

ASJC Scopus subject areas

Mathematics (miscellaneous)

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10.1007/s00028-008-0396-1

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title = "Asymptotic stability for the Navier-Stokes equations",

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).",

keywords = "Asymptotic stability, Besov spaces, Navier-Stokes equations",

author = "Jishan Fan and Tohru Ozawa",

note = "Funding Information: Mathematics Subject Classifications (2000): 76N15, 35Q30, 35Q35, 35M20 Key words: Asymptotic stability, Navier-Stokes equations, Besov spaces. ∗Supported by NSFC (Grant No. 10301014).",

year = "2008",

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AU - Fan, Jishan

AU - Ozawa, Tohru

N1 - Funding Information: Mathematics Subject Classifications (2000): 76N15, 35Q30, 35Q35, 35M20 Key words: Asymptotic stability, Navier-Stokes equations, Besov spaces. ∗Supported by NSFC (Grant No. 10301014).

PY - 2008/5

Y1 - 2008/5

N2 - 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).

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).

KW - Asymptotic stability

KW - Besov spaces

KW - Navier-Stokes equations

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Asymptotic stability for the Navier-Stokes equations

Abstract

Keywords

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