Remarks on the theory of Oldroyd-B fluids in exterior domains

Matthias Hieber

doi:10.3934/dcdss.2013.6.1307

Article Contents

2013, Volume 6, Issue 5: 1307-1313. Doi: 10.3934/dcdss.2013.6.1307

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Remarks on the theory of Oldroyd-B fluids in exterior domains

Matthias Hieber^1,

1.
Fachbereich Mathematik, Angewandte Analysis, Technische Universität Darmstadt, Schlossgartenstr. 7, 64289 Darmstadt

Received: November 30, 2011

Revised: February 29, 2012

Published: September 2013

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Abstract

Consider the set of equations describing Oldroyd-B fluids with finite Weissenberg numbers in exterior domains. In this note, we describe the main ideas of the proofs of two recent results on global existence for this set of equations on exterior domains subject to Dirichlet boundary conditions. The methods described here are quite different from the techniques used in the Lagrangian approach which is often used in the case of infinite Weissenberg numbers.

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Mathematics Subject Classification: 35Q35, 76D03, 76D05.

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