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Steady Stokes Flow in Exterior Domains

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Book cover An Introduction to the Mathematical Theory of the Navier-Stokes Equations

Part of the book series: Springer Tracts in Natural Philosophy ((STPHI,volume 38))

Abstract

In this chapter we shall analyse the Stokes problem in an exterior domain. Specifically, assuming that the region of flow Ω is a domain coinciding with the complement of a compact region (not necessarily connected) we wish to establish existence, uniqueness, and the validity of corresponding estimates for the velocity field v and the pressure field p of a steady flow in Ω governed by the Stokes approximation, i.e.,

$$\begin{gathered} \left. {\begin{array}{*{20}{c}} {\Delta v = \nabla p + f} \\ {\nabla \cdot v = 0} \\ \end{array} } \right\}in\Omega \hfill \\ v = {{v}_{*}}at\partial \Omega , \hfill \\ \end{gathered}$$
(0.1)

where f, v* are prescribed fields and where, as usual, we have taken the coefficient of kinematic viscosity to be one.

... Tu stesso ti fai grosso col falso immaginar, sì che non vedi ciò che vedresti, se l’aveeei scosso.

DANTE, Paradiso I, vv. 88–90.

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Notes for the Chapter

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  1. Istituto di Ingegneria, Università di Ferrara, Via Scandiana 21, 44100, Ferrara, Italy

    Giovanni P. Galdi

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  1. Giovanni P. Galdi
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Galdi, G.P. (1994). Steady Stokes Flow in Exterior Domains. In: An Introduction to the Mathematical Theory of the Navier-Stokes Equations. Springer Tracts in Natural Philosophy, vol 38. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-3866-7_5

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  • DOI: https://doi.org/10.1007/978-1-4757-3866-7_5

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  • Print ISBN: 978-1-4757-3868-1

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