Abstract
As we observed in the Introduction to Chapter V, the Stokes approximation fails to describe the physical properties of a system constituted by an object B moving with a small, constant velocity in a viscous liquid, at least at large distances from B where the viscous effects become less important. In particular, for B a ball, the explicit solution one finds (see (V.0.3)) exhibits no wake behind the body and is, therefore, unacceptable from the physical viewpoint. Moreover, for B a circle (plane motion), the problem admits no solution except for the trivial one. In addition to this, as observed by Oseen (1927, p.165), for the solution (V.0.3) we obtain, after a simple calculation,
no matter how small v∞ is, thus violating the assumption under which the Stokes equations are derived (see the Introduction to Chapter IV).
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e vidi le fiammelle andare avante, lasciando retro a sè l’aer dipinto.
DANTE, Purgatorio XXIX, vv. 73–74
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Bibliography
Fax6n, H., 1928/1929, Fredholm’sche Integraleichungen zu der Hydrodynamik Zäher Flüssigkeiten, Ark. Mat Astr. Fys(14) 21, 1–20 [Notes for VII]
Odqvist, F.K.G., 1930, Über die Randwertaufgaben der Hydrodynamik Zäher Flüssigkeiten, Math. Z., 32, 329–375 [IV.3, IV.6, IV.8, V.5, Notes for V]
Mikhlin, S.G., 1965, Multidimensional Singular Integrals and Integral Equations, Pergamon Press [V.3]
Salvi, R., 1991, The Exterior Problem for the Stationary Navier-Stokes Equations: On the Existence and Regularity, Navier-Stokes Equations: Theory and Numerical Methods, Heywood, J.G., Masuda, K., Rautmann, R., and Solonnikov V.A., Eds., Lecture Notes in Mathematics, Vol. 1530, Springer-Verlag, 132–145 [Notes for VII]
Serrin, J.B., 1961, Strong Convergence in a Product Space, Proc. Am. Math. Soc., 651–655 [Notes for II]
Kozono, H., and Sohr, H., 1992a, Density Properties for Solenoidal Vector Fields, with Applications to the Navier-Stokes Equations, J. Math. Soc. Japan„ 300, 307–330 [Notes for III]
Kratz, W., 1995a, The Maximum Modulus Theorem for the Stokes System in a Ball, Preprint, Universität Ulm [Notes for IV]
Pileckas, K., 1996a, Weighted ¿«-Solvability for the Steady Stokes System in Domains with Noncompact Boundaries, Math. Models and Methods in Appl. Sci.f 6, 97–136 [Introduction to VI]
Valli, A., 1985, On the Integral Representation of the Solution to the Stokes System, Rend. Sem. Mat. Padova, 74, 85–114 [Notes for IV]
Olmstead, W.E., and Gautesen, A.K., 1976, Integral Representations and the Oseen Flow Problem, Mechanics Today, Vol 3., Nemat-Nasser, S., Ed., Pergamon Press Inc., 125–189 [Notes to VII]
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© 1994 Springer Science+Business Media New York
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Galdi, G.P. (1994). Steady Oseen 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_7
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DOI: https://doi.org/10.1007/978-1-4757-3866-7_7
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