Abstract
In this chapter we give an overview of the equations of classical hydrodynamics. We provide their derivation, comment on the stress tensor, and thermodynamics, finally we present some elementary properties and also some exact solutions of the Navier–Stokes equations.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
D.J. Acheson, Elementary Fluid Dynamics (Oxford University Press, Oxford, 1990)
R. Aris, Vectors, Tensors and the Basic Equations of Fluid Mechanics (Prentice-Hall, Englewood Cliffs, NJ, 1962)
G.K. Batchelor, An Introduction to Fluid Dynamics (Cambridge University Press, New York, 2007)
G. Birkhoff, Hydrodynamics. A Study in Logic, Fact and Similitude (Princeton University Press, Princeton, NJ, 1960)
G.W. Bluman, S.C. Anco, Symmetry and Integration Methods for Differential Equations (Springer, New York, 2002)
B.J. Cantwell, Introduction to Symmetry Analysis (Cambridge University Press, Cambridge, 2002)
O. Darrigol, Worlds of Flows: A History of Hydrodynamics from Bernoullis to Prandtl (Oxford University Press, Oxford, 2005)
P.A. Davidson, Turbulence. An Introduction to Scientists and Engineers (Oxford University Press, Oxford, 2004)
Ch.R. Doering, J.D. Gibbon, Applied Analysis of the Navier-Stokes Equations (Cambridge University Press, Cambridge, 1995)
A.C. Eringen, Theory of micropolar fluids. J. Math. Mech. 16(1), 1–18 (1966)
G. Gallavotti, Foundations of Fluid Dynamics (Springer, Berlin, 2005)
L.D. Landau, E.M. Lifshitz, Fluid Mechanics, 2nd edn. Course of Theoretical Physics Series (Butterworth-Heinemann, Oxford, 1987)
G. Łukaszewicz, Micropolar Fluids. Theory and Applications (Birkhauser, Boston, 1999)
A.J. Majda, A.L. Bertozzi, Vorticity and Incompressible Flow (Cambridge University Press, Cambridge, 2002)
J. Serrin, Mathematical principles of classical fluid mechanics, in Fluid Mechanics I, ed. by C. Truesdell. Encyclopedia of Physics, Springer, Berlin, Heidelberg, vol. 3/8/1 (1959)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Łukaszewicz, G., Kalita, P. (2016). Equations of Classical Hydrodynamics. In: Navier–Stokes Equations. Advances in Mechanics and Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-27760-8_2
Download citation
DOI: https://doi.org/10.1007/978-3-319-27760-8_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-27758-5
Online ISBN: 978-3-319-27760-8
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)