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On the incompressible limit of the compressible Navier-Stokes equations

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1340)

Keywords

  • Compressible Fluid
  • Incompressible Limit
  • Quasilinear Hyperbolic System
  • Open Bounded Domain
  • Compressible Viscous Fluid

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References

  1. S. Agmon, A. Douglis and L. Nirenberg, Estimates near the boundary for solution of elliptic partial differential equations satisfying general boundary conditions, II, Comm. Pure Appl. Math 17 (1964), 35–92.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. H. Beirão da Veiga, Stationary motions and the incompressible limit for compressible viscous fluids, MRC Technical Summary Report #2883, Mathematics Research Center, University of Wisconsin-Madison, (1985); to appear in the Houston Journal of Mathematics.

    Google Scholar 

  3. H. Beirão da Veiga, An Lp-theory for the n-dimensional, stationary, compressible Navier-Stokes equations, and the incompressible limit for compressible fluids. The equilibrium solution, Communications in Mathematical Physics 109 (1987), 229–248.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. H. Beirão da Veiga, Existence results in Sobolev spaces for a stationary transport equation, to appear in Ricerche di Matematica in the volume in honour to Prof. C. Miranda. See also: On a stationary transport equation, Ann. Univ. Ferrara 32 (1986).

    Google Scholar 

  5. H. Beirão da Veiga, On a linear non-elliptic system concerning the dynamic of stationary motions, to appear in Rend. Sem. Mat. Fis. Milano.

    Google Scholar 

  6. A. De Franceschi, On the stationary, compressible and incompressible Navier-Stokes equations, to appear in Ann. Mat. Pura Appl..

    Google Scholar 

  7. S. Klainerman and A. Majda, Singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids, Comm. Pure App. Math. 34 (1981), 481–524.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. M. Padula, Existence and uniqueness for viscous steady compressible motions, to appear.

    Google Scholar 

  9. J. Serrin, Mathematical principles of classical fluid mechanics, Handbuch der Physik, Bd. VIII/1, Springer-Verlag, Berlin-Göttingen-Heidelberg (1959).

    Google Scholar 

  10. A. Valli, Periodic and stationary solutions for compressible Navier-Stokes equations via a stability method, Ann. Sc. Normale Sup. Pisa (1984), 607–647.

    Google Scholar 

  11. A. Valli, On the existence of stationary solutions to compressible Navier-Stokes equations, Ann. Inst. H. Poincaré, Anal. Non Lineaire (1986).

    Google Scholar 

  12. A. Valli and W.M. Zajaczkowski, Navier-Stokes equations for compressible fluids: Global existence and qualitative properties of the solutions in the general case, Comm. Math. Physics 103 (1986), 259–296.

    CrossRef  MathSciNet  MATH  Google Scholar 

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Dedicated to Hans Lewy

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© 1988 Springer-Verlag

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Beirão da Veiga, H. (1988). On the incompressible limit of the compressible Navier-Stokes equations. In: Hildebrandt, S., Kinderlehrer, D., Miranda, M. (eds) Calculus of Variations and Partial Differential Equations. Lecture Notes in Mathematics, vol 1340. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0082881

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  • DOI: https://doi.org/10.1007/BFb0082881

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-50119-0

  • Online ISBN: 978-3-540-45932-3

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