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Non stationary Navier-Stokes flows with vanishing viscosity

  • Bui An Ton
Article

Summary

An elementary proof that the solution of the Cauchy problem for the Navier-Stokes equations converges, in an appropriate sense, to the solution of the Euler equations on a small time interval is given. A partial result is given in the case of initial boundary-value problems.

Keywords

Weak Solution Cauchy Problem Euler Equation Constant Independent Reflexive Banach Space 
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References

  1. [1]
    Aubin J. P.,Un théoreme de compacité, C. R. Acad. Sc. Paris,256 (1963), 5042–5044.MATHMathSciNetGoogle Scholar
  2. [2]
    Ebin D. G. and Marsden J. E.,Groups of diffeomorphisms and the motion of an incompressible fluid, Ann. of Math., (2)97 (1970), 102–163.CrossRefMathSciNetGoogle Scholar
  3. [3]
    Golovkin K. K.,New equations modeling the motion of a viscous fluid and their unique solvability, Trudy Mat. Inst. Steklov,102 (1967), 29–50; Proc. Steklov Inst. Math.,102 (1967), 29–54.MathSciNetGoogle Scholar
  4. [4]
    Kato T.,Non stationary flows of viscous and ideal flows in R 3, J. Functional Analysis, (1972), 296–305.Google Scholar
  5. [5]
    Ladyzenskaya O. A.,New equations for the description of motion of viscous incompressible fluids and solvability in the large of boundary-value problems for them, Trudy Mat. Inst. Steklov102 (1967), 85–104; Proc. Steklov Inst. Math.102 (1967) 95–118.MathSciNetGoogle Scholar
  6. [6]
    —,The Mathematical theory of viscous incompressible fluids, Gordon and Breach, New York, 1969.Google Scholar
  7. [7]
    Lions J. L.,Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod, Paris, 1969.MATHGoogle Scholar
  8. [8]
    Swann H. S. G.,The convergence with vanishing viscosity of non stationary Navier-Stokes flow to ideal flow in R 3. Trans. Amer. Math. Soc.157 (1971), 373–397.MATHCrossRefMathSciNetGoogle Scholar
  9. [9]
    Visik M. I.,Quasi-linear strongly elliotic systems of differential equations in divergence form, Trudy Moskov Math. Obsc.12, (1963), 125 184; Trans. Moscov Math. Soc (1963), 140–208.MathSciNetGoogle Scholar

Copyright information

© Springer 1978

Authors and Affiliations

  • Bui An Ton
    • 1
  1. 1.Dept. of MathematicsUniversity of British ColumbiaVancouverCanada

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