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Milan Journal of Mathematics

, Volume 87, Issue 2, pp 169–199 | Cite as

Boundary Conditions for Planar Stokes Equations Inducing Vortices Around Concave Corners

  • Filippo GazzolaEmail author
  • Gianmarco Sperone
Article
  • 47 Downloads

Abstract

Fluid flows around an obstacle generate vortices which are difficult to locate and to describe. A variational formulation for a class of mixed and nonstandard boundary conditions on a smooth obstacle is discussed for the Stokes equations. Possible boundary data are then derived through separation of variables of biharmonic equations in a planar region having an internal concave corner. Explicit singular solutions show that, at least qualitatively, these conditions are able to reproduce vortices over the leeward wall of the obstacle.

Keywords

Planar Stokes equations mixed and nonstandard boundary conditions vortices 

Mathematics Subject Classification (2010)

35G15 76D07 76D17 

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Notes

Acknowledgements

The Authors are grateful to Andrei Fursikov (Moscow State University) for his valuable comments on a preliminary version of the present paper. The first Author is partially supported by the PRIN project Equazioni alle derivate parziali di tipo ellittico e parabolico: aspetti geometrici, disuguaglianze collegate, e applicazioni and by the Gruppo Nazionale per l’Analisi Matematica, la Probabilitàe le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM).

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Dipartimento di MatematicaPolitecnico di MilanoMilanoItaly

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