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Stability of solutions of the Navier-Stokes equations backward in time

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References

  • Bardos, C. & Tartar, L. 1973 Sur l'unicité retrograde des équations paraboliques et quelques questions voisines. Arch. Rational Mech. Anal. 50, 10–25.

    Google Scholar 

  • Cannon, J. R. & Knightly, G. H. 1970 Some continuous dependence theorems for viscous fluid motions. SIAM J. Appl. Math. 18, 627–640.

    Google Scholar 

  • Edmunds, D. E. 1963 On the uniqueness of viscous flows. Arch. Rational Mech. Anal. 14, 171–176.

    Google Scholar 

  • Fosdick, R. L. & Rajagopal, K. R. 1980 Thermodynamics and stability of fluids of third grade. Proc. Roy. Soc. London A 339, 351–377.

    Google Scholar 

  • Galdi, G. P. & Maremonti, P. 1986 A uniqueness theorem for viscous fluid motions in exterior domains. Arch. Rational Mech. Anal. 91, 375–384.

    Google Scholar 

  • Galdi, G. P. & Rionero, S. 1983 Local estimates and stability of viscous flows in an exterior domain. Arch. Rational Mech. Anal. 81, 333–347.

    Google Scholar 

  • Galdi, G. P. & Rionero, S. 1985 Weighted energy methods in fluid dynamics and elasticity. Springer-Verlag.

  • Ghidaglia, J. M. 1986 Some backward uniqueness results. Nonlin. Anal. Thy. Meth. Applicns. 10, 777–790.

    Google Scholar 

  • Knops, R. J. & Payne, L. E. 1968 On the stability of solutions of the Navier-Stokes equations backward in time. Arch. Rational Mech. Anal. 29, 331–335.

    Google Scholar 

  • Lees, M. & Protter, M. H. 1961 Unique continuation for parabolic differential equations and differential inequalities. Duke Math. J. 28, 369–382.

    Google Scholar 

  • Payne, L. E. 1971 Uniqueness and continuous dependence criteria for the Navier-Stokes equations. Rocky Mtn. J. Math. 2, 641–660.

    Google Scholar 

  • Serrin, J. 1963 The initial value problem for the Navier-Stokes equations. Article in, “Nonlinear Problems”. Madison: Univ. Wisconsin Press.

    Google Scholar 

  • Straughan, B. 1976 Global nonexistence of solutions to Ladyzhenskaya's variants of the Navier-Stokes equations backward in time. Proc. Roy. Soc. Edinburgh A 75, 165–170.

    Google Scholar 

  • Straughan, B. 1977 Uniqueness and continuous dependence theorems for the conduction-diffusion solution to the Boussinesq equations on an exterior domain. J. Math. Anal. Appl. 57, 203–233.

    Google Scholar 

  • Straughan, B. 1982 Nonexistence, instability and weighted energy methods in fluid dynamics and related theories. Pitman Press: London.

    Google Scholar 

  • Straughan, B. 1983 Backward uniqueness and unique continuation for solutions to the Navier-Stokes equations on an exterior domain. J. Math. pures et appl. 62, 49–62.

    Google Scholar 

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Authors and Affiliations

  1. Dipartimento de Matematica, Università di Ferrara, Italy

    G. P. Galdi & B. Straughan

  2. Department of Mathematics, University of Glasgow, Glasgow

    G. P. Galdi & B. Straughan

Authors
  1. G. P. Galdi
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  2. B. Straughan
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Communicated by J. Serrin

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Galdi, G.P., Straughan, B. Stability of solutions of the Navier-Stokes equations backward in time. Arch. Rational Mech. Anal. 101, 107–114 (1988). https://doi.org/10.1007/BF00251456

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  • DOI: https://doi.org/10.1007/BF00251456

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