Continuum Mechanics and Thermodynamics

, Volume 28, Issue 5, pp 1411–1419 | Cite as

The Oberbeck–Boussinesq approximation as a constitutive limit

  • Yoshiyuki Kagei
  • Michael Růžička
Original Article


We derive the usual Oberbeck–Boussinesq approximation as a constitutive limit of the full system describing the motion of an compressible linearly viscous fluid. To this end, the starting system is written, using the Gibbs free energy, in the variables v, θ and p. The Oberbeck–Boussinesq system is then obtained as the thermal expansion coefficient α and the isothermal compressibility coefficient β tend to zero.


Oberbeck–Boussinesq approximation Constitutive limit Gibbs free energy 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Faculty of MathematicsKyushu UniversityFukuokaJapan
  2. 2.Institute of Applied MathematicsUniversity of FreiburgFreiburgGermany

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