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Journal of Mathematical Fluid Mechanics

, Volume 14, Issue 2, pp 295–309 | Cite as

On the 3D Steady Flow of a Second Grade Fluid Past an Obstacle

  • Paweł Konieczny
  • Ondřej KremlEmail author
Article

Abstract

We study steady flow of a second grade fluid past an obstacle in three space dimensions. We prove existence of solution in weighted Lebesgue spaces with anisotropic weights and thus existence of the wake region behind the obstacle. We use properties of the fundamental Oseen tensor together with results achieved in Koch (Quad Mat 15:59–122, 2004) and properties of solutions to steady transport equation to get up to arbitrarily small ε the same decay as the Oseen fundamental solution.

Mathematics Subject Classification (2010)

35Q35 76D03 

Keywords

Second grade fluid Steady flow past an obstacle Asymptotic behavior Weighted estimates 

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Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  1. 1.Institute for Mathematics and its ApplicationsUniversity of MinnesotaMinneapolisUSA
  2. 2.Mathematical Institute of Charles UniversityPraha 8Czech Republic

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