The Navier–Stokes Equations as Model for Incompressible Flows

  • Volker John
Part of the Springer Series in Computational Mathematics book series (SSCM, volume 51)


The basic equations of fluid dynamics are called Navier–Stokes equations. In the case of an isothermal flow, i.e., a flow at constant temperature, they represent two physical conservation laws: the conservation of mass and the conservation of linear momentum. There are various ways for deriving these equations. Here, the classical one of continuum mechanics will be outlined. This approach contains some heuristic steps.


Dimensionless Navier-Stokes Equations Incompressible Flow Physical Conservation Laws Isothermal Flow Heuristic Step 
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  1. Bernardi C, Chacón Rebollo T, Yakoubi D (2015) Finite element discretization of the Stokes and Navier-Stokes equations with boundary conditions on the pressure. SIAM J Numer Anal 53:1256–1279MathSciNetCrossRefzbMATHGoogle Scholar
  2. Braack M, Mucha PB (2014) Directional do-nothing condition for the Navier-Stokes equations. J Comput Math 32:507–521MathSciNetCrossRefzbMATHGoogle Scholar
  3. Heywood JG, Rannacher R, Turek S (1996) Artificial boundaries and flux and pressure conditions for the incompressible Navier-Stokes equations. Int J Numer Methods Fluids 22:325–352MathSciNetCrossRefzbMATHGoogle Scholar
  4. Maxwell J (1879) On stresses in rarified gases arising from inequalities of temperature Philos Trans R Soc 170:231–256Google Scholar
  5. Navier C (1823) Mémoire sur les lois du mouvement des fluiales. Mém Acad R Soc 6:389–440Google Scholar
  6. Temam R (1995) Navier-Stokes equations and nonlinear functional analysis. CBMS-NSF regional conference series in applied mathematics, vol 66, 2nd edn. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, pp xiv+141Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Volker John
    • 1
    • 2
  1. 1.Weierstrass Institute for Applied Analysis and StochasticsBerlinGermany
  2. 2.Fachbereich Mathematik und InformatikFreie Universität BerlinBerlinGermany

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