Skip to main content
SpringerLink
Log in

A coupling between a 1D compressible-incompressible limit and the 1D p-system in the non smooth case

  • Published:
Bulletin of the Brazilian Mathematical Society, New Series Aims and scope Submit manuscript

Abstract

We consider two compressible immiscible fluids in one space dimension and in the isentropic approximation. The first fluid is surrounded and in contact with the second one. As the sound speed of the first fluid diverges to infinity, we prove the rigorous convergence for the compressible to incompressible limit of the coupled dynamic of the two fluids.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. D. Amadori and G. Guerra. Global BV solutions and relaxation limit for a system of conservation laws. Proc. Roy. Soc. Edinburgh Sect. A, 131(1) (2001), 1–26.

    Article  MathSciNet  MATH  Google Scholar 

  2. R. Borsche, R.M. Colombo and M. Garavello. Mixed systems: ODEs–balance laws. J. Differential Equations, 252(3) (2012), 2311–2338.

    Article  MathSciNet  MATH  Google Scholar 

  3. A. Bressan. Hyperbolic systems of conservation laws, volume 20 of Oxford Lecture Series in Mathematics and its Applications. Oxford University Press, Oxford, (2000). The one-dimensional Cauchy problem.

    Google Scholar 

  4. R.M. Colombo and G. Guerra. A coupling between a non-linear 1d compressibleincompressible limit and the 1d p-system in the non smooth case. Netw. Heterog. Media, 2016. To appear.

    Google Scholar 

  5. R.M. Colombo, G. Guerra and V. Schleper. The Compressible to Incompressible Limit of One Dimensional Euler Equations: The Non Smooth Case. Arch. Ration. Mech. Anal., 219(2) (2016), 701–718.

    Article  MathSciNet  MATH  Google Scholar 

  6. R.M. Colombo and V. Schleper. Two-phase flows: non-smooth well posedness and the compressible to incompressible limit. Nonlinear Anal. Real World Appl., 13(5) (2012), 2195–2213.

    Article  MathSciNet  MATH  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 Appl. Math., 34(4) (1981), 481–524.

    Article  MathSciNet  MATH  Google Scholar 

  8. S. Klainerman and A. Majda. Compressible and incompressible fluids. Comm. Pure Appl. Math., 35(5) (1982), 629–651.

    Article  MathSciNet  MATH  Google Scholar 

  9. G. Métivier and S. Schochet. The incompressible limit of the non-isentropic Euler equations. Arch. Ration. Mech. Anal., 158(1) (2001), 61–90.

    Article  MathSciNet  MATH  Google Scholar 

  10. G. Métivier and S. Schochet. The incompressible limit of the non-isentropic Euler equations. Arch. Ration. Mech. Anal., 158(1) (2001), 61–90.

    Article  MathSciNet  MATH  Google Scholar 

  11. S. Schochet. The compressible Euler equations in a bounded domain: existence of solutions and the incompressible limit. Comm. Math. Phys., 104(1) (1986), 49–75.

    Article  MathSciNet  MATH  Google Scholar 

  12. S. Schochet. The mathematical theory of low Mach number flows. M2AN Math. Model. Numer. Anal., 39(3) (2005), 441–458.

    Article  MathSciNet  MATH  Google Scholar 

  13. J. Xu and W.-A. Yong. A note on incompressible limit for compressible Euler equations. Math. Methods Appl. Sci., 34(7) (2011), 831–838.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dip. di Matematica e Applicazioni, Università di Milano-Bicocca, Milan, Italy

    Graziano Guerra

  2. Institute for Applied Analysis and Numerical Simulations, University of Stuttgart, Stuttgart, Germany

    Veronika Schleper

Authors
  1. Graziano Guerra
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Veronika Schleper
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Graziano Guerra.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Guerra, G., Schleper, V. A coupling between a 1D compressible-incompressible limit and the 1D p-system in the non smooth case. Bull Braz Math Soc, New Series 47, 381–396 (2016). https://doi.org/10.1007/s00574-016-0146-x

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00574-016-0146-x

Keywords

Mathematical subject classification

Search

Navigation