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

Vladimír Šverák, Tai Peng Tsai

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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 languageEnglish (US)
Pages (from-to)2107-2117
Number of pages11
JournalCommunications in Partial Differential Equations
Issue number11-12
StatePublished - 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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