On the spatial decay of 3-D steady-state Navier-Stokes flows

Vladimír Šverák; Tai Peng Tsai

doi:10.1080/03605300008821579

On the spatial decay of 3-D steady-state Navier-Stokes flows

Vladimír Šverák, Tai Peng Tsai

School of Mathematics

Research output: Contribution to journal › Article › peer-review

25 Scopus citations

Abstract

This note shows that any solution u of the Navier-Stokes equations in a 3-D exterior domain which decays as O(|x|^-1) at ∞ has the optimal decay ∇^ku(x) = O(|x|^-1-k) for k > 1, if the body force f satisfies ∇^mf(x) = O(|x|^-3-m) for all m < k. The main tool is an interior estimate for the Stokes system.

Original language	English (US)
Pages (from-to)	2107-2117
Number of pages	11
Journal	Communications in Partial Differential Equations
Volume	25
Issue number	11-12
DOIs	https://doi.org/10.1080/03605300008821579
State	Published - 2000

Bibliographical note

Funding Information:
We thank G. P. Galdi and T. Miyakawa for helpful remarks. Both authors were partially supported by NSF grant DhIS-9622795. The second author was also supported by a Sloan Foundation Dissertation Fellowship.

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title = "On the spatial decay of 3-D steady-state Navier-Stokes flows",

abstract = "This note shows that any solution u of the Navier-Stokes equations in a 3-D exterior domain which decays as O(|x|-1) at ∞ has the optimal decay ∇ku(x) = O(|x|-1-k) for k > 1, if the body force f satisfies ∇mf(x) = O(|x|-3-m) for all m < k. The main tool is an interior estimate for the Stokes system.",

author = "Vladim{\'i}r {\v S}ver{\'a}k and Tsai, {Tai Peng}",

note = "Funding Information: We thank G. P. Galdi and T. Miyakawa for helpful remarks. Both authors were partially supported by NSF grant DhIS-9622795. The second author was also supported by a Sloan Foundation Dissertation Fellowship.",

year = "2000",

doi = "10.1080/03605300008821579",

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journal = "Communications in Partial Differential Equations",

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T1 - On the spatial decay of 3-D steady-state Navier-Stokes flows

AU - Šverák, Vladimír

AU - Tsai, Tai Peng

N1 - Funding Information: We thank G. P. Galdi and T. Miyakawa for helpful remarks. Both authors were partially supported by NSF grant DhIS-9622795. The second author was also supported by a Sloan Foundation Dissertation Fellowship.

PY - 2000

Y1 - 2000

N2 - This note shows that any solution u of the Navier-Stokes equations in a 3-D exterior domain which decays as O(|x|-1) at ∞ has the optimal decay ∇ku(x) = O(|x|-1-k) for k > 1, if the body force f satisfies ∇mf(x) = O(|x|-3-m) for all m < k. The main tool is an interior estimate for the Stokes system.

AB - This note shows that any solution u of the Navier-Stokes equations in a 3-D exterior domain which decays as O(|x|-1) at ∞ has the optimal decay ∇ku(x) = O(|x|-1-k) for k > 1, if the body force f satisfies ∇mf(x) = O(|x|-3-m) for all m < k. The main tool is an interior estimate for the Stokes system.

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U2 - 10.1080/03605300008821579

DO - 10.1080/03605300008821579

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SN - 0360-5302

VL - 25

SP - 2107

EP - 2117

JO - Communications in Partial Differential Equations

JF - Communications in Partial Differential Equations

IS - 11-12

ER -

On the spatial decay of 3-D steady-state Navier-Stokes flows

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