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The Oberbeck–Boussinesq Approximation as a Singular Limit of the Full Navier–Stokes–Fourier System

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Abstract.

We consider the asymptotic limit for the complete Navier–Stokes–Fourier system as both Mach and Froude numbers tend to zero. The limit is investigated in the context of weak variational solutions on an arbitrary large time interval and for the ill-prepared initial data. The convergence to the Oberbeck–Boussinesq system is shown.

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Authors and Affiliations

  1. Mathematical Institute of the Academy of Sciences of the Czech Republic, Žitná 25, 115 67, Praha 1, Czech Republic

    Eduard Feireisl

  2. Université du Sud Toulon-Var, BP 20132, 83957, La Garde, France

    Antonin Novotný

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  1. Eduard Feireisl
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  2. Antonin Novotný
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Correspondence to Eduard Feireisl.

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Communicated by I. Straškraba

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Feireisl, E., Novotný, A. The Oberbeck–Boussinesq Approximation as a Singular Limit of the Full Navier–Stokes–Fourier System. J. math. fluid mech. 11, 274–302 (2009). https://doi.org/10.1007/s00021-007-0259-5

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  • DOI: https://doi.org/10.1007/s00021-007-0259-5

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