Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

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

Pages: 2757 - 2776, Volume 33, Issue 7, July 2013      doi:10.3934/dcds.2013.33.2757

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Paul Deuring - Univ Lille Nord de France, 59000 Lille, France (email)

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.

Keywords:  Exterior domain, time-dependent Oseen system, pointwise decay.
Mathematics Subject Classification:  Primary: 35Q30, 65N30; Secondary: 76D05.

Received: April 2012;      Revised: November 2012;      Available Online: January 2013.