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Global Weak Solutions to the Full Compressible Navier-Stokes Equations with Spherically Symmetric Data in a 2-D Ball

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Abstract

In this paper, we prove the global existence of weak solutions to the viscous and heat-conductive compressible Navier-Stokes systems in a two dimension ball with spherically symmetric initial data.

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References

  1. Antontsev, S.N., Kazhikhov, A.V., Monakhov, V.N.: Boundary Value Problems in Mechanics of Nonhomogeneous Fluids. North-Holland, Amsterdam (1990)

    MATH  Google Scholar 

  2. Feireisl, E., Novotný, A., Petzeltová, H.: On the existence of globally defined weak solutions to the Navier-Stokes equations of isentropic compressible fluids. J. Math. Fluid Mech. 3, 358–392 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  3. Feireisl, E.: Dynamics of Viscous Compressible Fluids. Oxford Lecture Series in Mathematics and Its Applications, vol. 26. Oxford University Press, Oxford (2004)

    MATH  Google Scholar 

  4. Feireisl, E.: On the motion of a viscous, compressible, and heat conducting fluid. Indiana Univ. Math. J. 53, 1705–1738 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  5. Feireisl, E.: Mathematical theory of compressible, viscous, and heat conducting fluids. Comput. Math. Appl. 53, 461–490 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  6. Hoff, D.: Spherically symmetric solutions of the Navier-Stokes equations for compressible, isothermal flow with large discontinuous initial data. Indiana Univ. Math. J. 41, 1225–1302 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  7. Hoff, D.: Global solutions of the Navier-Stokes equations for multidimensional compressible flow with discontinuous initial data. J. Differ. Equ. 120, 215–254 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  8. Hoff, D., Jenssen, H.K.: Symmetric nonbarotropic flows with large data and forces. Arch. Ration. Mech. Anal. 173, 297–343 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  9. Jiang, F., Jiang, S., Yin, J.: Global weak solutions to the two-dimensional Navier-Stokes equations of compressible heat-conducting flows with symmetric data and forces. Discrete Contin. Dyn. Syst. 34(2), 567–587 (2014)

    MATH  MathSciNet  Google Scholar 

  10. Jiang, L., Wang, C.: Global weak solutions to the compressible Navier-Stokes equations in the exterior domain with spherically symmetric data. Acta Appl. Math. 121, 197–211 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  11. Jiang, S.: Global spherically symmetric solutions to the equations of a viscous polytropic ideal gas in an exterior domain. Commun. Math. Phys. 178, 339–374 (1996)

    Article  MATH  Google Scholar 

  12. Jiang, S., Zhang, P.: On spherically symmetric solutions of the compressible isentropic Navier-Stokes equations. Commun. Math. Phys. 215, 559–581 (2001)

    Article  MATH  Google Scholar 

  13. Jiang, S., Zhang, P.: Global weak solutions to the Navier-Stokes equation for a 1D viscous polytropic ideal gas. Q. Appl. Math. 61, 435–449 (2003)

    MATH  Google Scholar 

  14. Kazhikhov, A.V., Shelukhin, V.V.: Unique global solution with respect to time of initial boundary value problems for one-dimensional equations of a viscous gas. J. Appl. Math. Mech. 41, 273–282 (1977)

    Article  MathSciNet  Google Scholar 

  15. Lions, P.L.: Mathematical Topics in Fluid Mechanics. Volume 2: Compressible Models. Oxford University Press, London (1998)

    Google Scholar 

  16. Matsumura, A., Nishida, T.: The initial value problem for the equations of motion of viscous and heat-conductive gases. J. Math. Kyoto Univ. 20, 67–104 (1980)

    MATH  MathSciNet  Google Scholar 

  17. Matsumura, A., Nishida, T.: Initial boundary value problems for the equations of motion of compressible viscous and heat-conductive fluids. Commun. Math. Phys. 89, 445–464 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  18. Serre, D.: Sur l’équation monodimensionnelle d’un fluids visqueux, compressible et conducteur de chaleur. C. R. Acad. Sci. Paris, Sér. I 303, 703–706 (1986)

    MATH  Google Scholar 

  19. Xin, Z.: Blow-up of smooth solutions to the compressible Navier-Stokes equations with compact density. Commun. Pure Appl. Math. 51, 229–240 (1998)

    Article  MATH  Google Scholar 

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Acknowledgements

We would like to thank to Prof. Ping Zhang and Prof. Zhifei Zhang for the profitable discussions and suggestions about this topic.

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Authors and Affiliations

  1. Department of Mathematics, Central University of Finances and Economics, Beijing, 100081, China

    Donghong Li

  2. Beijing International Center For Mathematical Research, Peking University, Beijing, 100871, China

    Chao Wang

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  1. Donghong Li
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  2. Chao Wang
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Correspondence to Chao Wang.

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Li, D., Wang, C. Global Weak Solutions to the Full Compressible Navier-Stokes Equations with Spherically Symmetric Data in a 2-D Ball. Acta Appl Math 140, 111–131 (2015). https://doi.org/10.1007/s10440-014-9981-1

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  • DOI: https://doi.org/10.1007/s10440-014-9981-1

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