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The steady state Stefan problem with convection

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Abstract

For steady-state Stefan problems with convection in the fluid phase governed by either the Stokes equations or the Navier Stokes equations, and with adherence of the fluid on all boundaries, the existence of a weak solution is obtained via the introduction of a temperature dependent penalty term in the fluid flow equation together with application of various compactness arguments.

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References

  1. Gilbarg, D., & N. S. Trudinger, Elliptic Partial Differential Equations of Second Order. New York: Springer 1977.

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  2. Ladyzhenskaya, O. A., The Mathematical Theory of Viscous Incompressible Flow. 2nd Edition. New York: Gordon and Breach 1969.

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  3. Ladyzhenskaya, O. A., & N. N. Ural'tseva, Linear and Quasilinear Elliptic Equations. New York: Academic Press 1968.

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Authors and Affiliations

  1. Department of Mathematics, University of Texas, Austin

    J. R. Cannon, Emmanuele DiBenedetto & George H. Knightly

  2. Department of Mathematics, University of Massachusetts, Amherst

    J. R. Cannon, Emmanuele DiBenedetto & George H. Knightly

Authors
  1. J. R. Cannon
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  2. Emmanuele DiBenedetto
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  3. George H. Knightly
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Additional information

Communicated by J. Serrin

This research was supported in part by the National Science Foundation and the Consiglio Nazionale delle Ricerche.

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Cannon, J.R., DiBenedetto, E. & Knightly, G.H. The steady state Stefan problem with convection. Arch. Rational Mech. Anal. 73, 79–97 (1980). https://doi.org/10.1007/BF00283258

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  • DOI: https://doi.org/10.1007/BF00283258

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