Skip to main content
SpringerLink
Log in

Local Well-Posedness of Dynamics of Viscous Gaseous Stars

  • Published:
Archive for Rational Mechanics and Analysis Aims and scope Submit manuscript

Abstract

We establish the local-in-time well-posedness of strong solutions to the vacuum free boundary problem of the compressible Navier–Stokes–Poisson system in the spherically symmetric and isentropic motion. Our result captures the physical vacuum boundary behavior of the Lane–Emden star configurations for all adiabatic exponents \({\gamma < \frac{6}{5}}\) .

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. Chandrasekhar S.: An Introduction to the Study of Stellar Structures. University of Chicago Press, Chicago (1938)

    Google Scholar 

  2. Deng Y., Liu T.-P., Yang T., Yao Z.-A.: Solutions of Euler–Poisson equations for gaseous stars. Arch. Rational Mech. Anal. 164, 261–285 (2002)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  3. Ducomet B., Zlotnik A.: Stabilization and stability for the spherically symmetric Navier–Stokes–Poisson system. Appl. Math. Lett. 18, 1190–1198 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  4. Evans L.: Partial Differential Equations, vol 19. American Mathematical Society, Providence (1998)

    Google Scholar 

  5. Jang J.: Nonlinear instability in gravitational Euler–Poisson system for \({\gamma=\frac{6}{5}}\) . Arch. Rational Mech. Anal. 188, 265–307 (2008)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  6. Lin S.-S.: Stability of gaseous stars in spherically symmetric motions. SIAM J. Math. Anal. 28, 539–569 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  7. Luo T., Xin Z., Yang T.: Interface behavior of compressible Navier–Stokes equations with vacuum. SIAM J. Math. Anal. 31, 1175–1191 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  8. Makino T.: On a local existence theorem for the evolution equation of gaseous stars. Patterns and waves. Stud. Math. Appl. 18, 459–479 (1986)

    MathSciNet  Google Scholar 

  9. Matusu-Necasova S., Okada M., Makino T.: Free boundary problem for the equation of spherically symmetric motion of viscous gas III. Jpn. J. Ind. Appl. Math. 14, 199–213 (1997)

    Article  MathSciNet  Google Scholar 

  10. Okada M., Makino T.: Free boundary problem for the equation of spherically symmetric motion of viscous gas. Jpn. J. Ind. Appl. Math. 10, 219–235 (1993)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Courant Institute of Mathematical Sciences, New York, NY, USA

    Juhi Jang

Authors
  1. Juhi Jang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Juhi Jang.

Additional information

Communicated by C. M. Dafermos

Rights and permissions

Reprints and permissions

About this article

Cite this article

Jang, J. Local Well-Posedness of Dynamics of Viscous Gaseous Stars. Arch Rational Mech Anal 195, 797–863 (2010). https://doi.org/10.1007/s00205-009-0253-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00205-009-0253-6

Keywords

Search

Navigation