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Uniqueness criteria for the conduction-diffusion solution of the Boussinesq equations

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References

  1. Joseph, D.D., Nonlinear stability of the Boussinesq equations by the method of energy. Arch. Rational Mech. Anal. (3) 22, 163–184 (1966).

    Google Scholar 

  2. Serrin, J., On the stability of viscous fluid motions. Arch. Rational Mech. Anal. (1) 3, 1–13 (1959).

    Google Scholar 

  3. Shir, C. C., & D. D. Joseph, Convective instability in temperature and concentration field. Arch. Rational Mech. Anal. (1) 30, 38–80 (1968).

    Google Scholar 

  4. Veronis, G., On finite-amplitude instability in the thermohaline convection. J. Marine Res. (1), 23 (1964).

  5. Veronis, G., Effect of a stabilizing gradient of solute on thermal convection. J. Fluid Mech. 34, 315–337 (1968).

    Google Scholar 

  6. Sani, R., On finite amplitude roll cell disturbances in a fluid layer subjected to heat and mass transfer. A. I. Ch. E. Journal (6) 11 (1965).

  7. Busse, F., The stability of finite amplitude cellular convection and its relation to an extremum principle. J. Fluid Mech. 30, 625–649 (1967).

    Google Scholar 

  8. Fife, P., & D. D. Joseph, Existence of convective solutions of the generalized Bénard problem which are analytic in their norm. Arch. Rational Mech. Anal. (2) 33, 116–138 (1969).

    Google Scholar 

  9. Sani, R., Ph. D. Thesis, Department of Chemical Engineering, University of Minnesota, Minneapolis, 1963.

    Google Scholar 

  10. Prodi, G., Teoremi di tipo locale, per il sistema di Navier-Stokes e stabilità délle soluzioni stazionarie. Rend. Sem. Mat. Univ. Padova 32 (1962).

  11. Turner, J., & H. Stommel, A new case of convection in the presence of combined vertical salinity and temperature gradients. Proc. U. S. Nat. Acad. Sci. 52, 49–53 (1968).

    Google Scholar 

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Communicated by C. Truesdell

This work was partly supported under the U.S. National Science Foundation grant GK 1838.

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Joseph, D.D. Uniqueness criteria for the conduction-diffusion solution of the Boussinesq equations. Arch. Rational Mech. Anal. 35, 169–177 (1969). https://doi.org/10.1007/BF00247511

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  • DOI: https://doi.org/10.1007/BF00247511

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