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Equations of Classical Hydrodynamics

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Navier–Stokes Equations

Part of the book series: Advances in Mechanics and Mathematics ((AMMA))

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.

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References

  1. D.J. Acheson, Elementary Fluid Dynamics (Oxford University Press, Oxford, 1990)

    MATH  Google Scholar 

  2. R. Aris, Vectors, Tensors and the Basic Equations of Fluid Mechanics (Prentice-Hall, Englewood Cliffs, NJ, 1962)

    MATH  Google Scholar 

  3. G.K. Batchelor, An Introduction to Fluid Dynamics (Cambridge University Press, New York, 2007)

    MATH  Google Scholar 

  4. G. Birkhoff, Hydrodynamics. A Study in Logic, Fact and Similitude (Princeton University Press, Princeton, NJ, 1960)

    Google Scholar 

  5. G.W. Bluman, S.C. Anco, Symmetry and Integration Methods for Differential Equations (Springer, New York, 2002)

    MATH  Google Scholar 

  6. B.J. Cantwell, Introduction to Symmetry Analysis (Cambridge University Press, Cambridge, 2002)

    MATH  Google Scholar 

  7. O. Darrigol, Worlds of Flows: A History of Hydrodynamics from Bernoullis to Prandtl (Oxford University Press, Oxford, 2005)

    MATH  Google Scholar 

  8. P.A. Davidson, Turbulence. An Introduction to Scientists and Engineers (Oxford University Press, Oxford, 2004)

    Google Scholar 

  9. Ch.R. Doering, J.D. Gibbon, Applied Analysis of the Navier-Stokes Equations (Cambridge University Press, Cambridge, 1995)

    Book  MATH  Google Scholar 

  10. A.C. Eringen, Theory of micropolar fluids. J. Math. Mech. 16(1), 1–18 (1966)

    MathSciNet  Google Scholar 

  11. G. Gallavotti, Foundations of Fluid Dynamics (Springer, Berlin, 2005)

    MATH  Google Scholar 

  12. L.D. Landau, E.M. Lifshitz, Fluid Mechanics, 2nd edn. Course of Theoretical Physics Series (Butterworth-Heinemann, Oxford, 1987)

    MATH  Google Scholar 

  13. G. Łukaszewicz, Micropolar Fluids. Theory and Applications (Birkhauser, Boston, 1999)

    Google Scholar 

  14. A.J. Majda, A.L. Bertozzi, Vorticity and Incompressible Flow (Cambridge University Press, Cambridge, 2002)

    MATH  Google Scholar 

  15. 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)

    Google Scholar 

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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

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