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On Nonlinear Rayleigh–Taylor Instabilities

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Abstract

Some of the mathematical properties of the interface between two incompressible inviscid and immiscible fluids with different densities under the influence of a constant gravity field g are investigated. The purpose of this paper is to prove that linearly unstable modes for Rayleigh–Taylor instabilities give birth to nonlinear instabilities for the full nonlinear system. The main ingredient is a general instability theorem in an analytic framework which enables us to go from linear to nonlinear instabilities.

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References

  1. Chandrasekhar, S.: Hydrodynamic and Hydromagnetic Stability, Oxford Univ. Press, London, 1968

  2. Drazin, P. G., Reid, W. H.: Hydrodynamic Stability, Cambridge Univ. Press, 1981

  3. Mikaelian, K. O.: Connection between the Rayleigh and the Schrödinger equations. Phys. Rev. E, 53, 3551 (1996)

    Article  MathSciNet  Google Scholar 

  4. Sulem, C., Sulem, P. L.: Finite time analyticity for the two and three dimensionnal Rayleigh Taylor instability. Trans. Amer. Math. Soc., 287(1), 127–160 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  5. Desjardins, B., Grenier, E: Linear instability implies nonlinear stability for various boundary layers, Annales de l’Institut Henri Poincare (C) Non Linear Analysis, Volume 20, Issue 1

  6. Caflish, R. E.: A simplified version of the abstract Cauchy–Kowalewski theorem with weak singularities. Bull. Amer. Math. Soc. (N. S.), 23(2), 495–500 (1990)

    Article  MathSciNet  Google Scholar 

  7. Sammartino, M., Caflish, R. E.: Zero viscosity limit for analytic solutions, of the Navier-Stokes equation on a half-space. I. Existence for Euler and Prandtl equations. Comm. Math. Phys., 192(2), 433–461 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  8. Schlichting, H.: Boundary Layer Theory, Schlichting, Boundary Layer Theory, McGraw–Hill, New York, 1968

  9. Cherfils, C., Lafitte, O.: Analytic solutions of the Rayleigh equation for linear density profiles. Phys. Rev. E, 62, 2967 (2000)

    Article  Google Scholar 

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Authors and Affiliations

  1. CEA/DIF, B. P. 12, 91680, Bruyères le Châtel, France

    B. Desjardins

  2. U.M.P.A., C.N.R.S.U.M.R. 5669, Ecole Normale Supérieure de Lyon, 69364, Lyon cedex 7, France

    E. Grenier

Authors
  1. B. Desjardins
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  2. E. Grenier
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Correspondence to B. Desjardins.

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Desjardins, B., Grenier, E. On Nonlinear Rayleigh–Taylor Instabilities. Acta Math Sinica 22, 1007–1016 (2006). https://doi.org/10.1007/s10114-005-0559-8

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  • DOI: https://doi.org/10.1007/s10114-005-0559-8

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