Pointwise spatial decay of time-dependent Oseen flows: The case of data with noncompact support

Paul Deuring

doi:10.3934/dcds.2013.33.2757

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2013, Volume 33, Issue 7: 2757-2776. Doi: 10.3934/dcds.2013.33.2757

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Pointwise spatial decay of time-dependent Oseen flows: The case of data with noncompact support

Paul Deuring^1,

1.
Univ Lille Nord de France, 59000 Lille

Received: March 31, 2012

Revised: October 31, 2012

Published: June 2013

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Abstract

The article deals with the time-dependent Oseen system in a 3D exterior domain. It is shown that the velocity part of a weak solution to that system decays as $\bigl(\, |x| \cdot (1+|x|-x_1) \,\bigr) ^{-1}$, and its spatial gradient as $\bigl(\, |x| \cdot (1+|x|-x_1) \,\bigr) ^{-3/2}$, for $|x|\to \infty $. This result is obtained for data that need not have compact support.

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Mathematics Subject Classification: Primary: 35Q30, 65N30; Secondary: 76D05.

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