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The Scientific World Journal
Volume 2016, Article ID 3781760, 6 pages
http://dx.doi.org/10.1155/2016/3781760
Research Article

Blowup Phenomenon of Solutions for the IBVP of the Compressible Euler Equations in Spherical Symmetry

Department of Mathematics and Information Technology, The Hong Kong Institute of Education, 10 Lo Ping Road, Tai Po, New Territories, Hong Kong

Received 3 December 2015; Accepted 19 January 2016

Academic Editor: Martin Bohner

Copyright © 2016 Ka Luen Cheung and Sen Wong. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. P. L. Lions, Mathematical Topics in Fluid Mechanics, vol. 1, Clarendon Press, Oxford, UK, 1998.
  2. P. L. Lions, Mathematical Topics in Fluid Mechanics, vol. 2, Clarendon Press, Oxford, UK, 1998.
  3. X. Zhu and A. Tu, “Blowup of the axis-symmetric solutions for the IBVP of the isentropic Euler equations,” Nonlinear Analysis, vol. 95, pp. 99–106, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. X. Zhu, “Blowup of the solutions for the IBVP of the isentropic Euler equations with damping,” Journal of Mathematical Analysis and Applications, vol. 432, no. 2, pp. 715–724, 2015. View at Publisher · View at Google Scholar · View at MathSciNet
  5. T. C. Sideris, “Formation of singularities in three-dimensional compressible fluids,” Communications in Mathematical Physics, vol. 101, no. 4, pp. 475–485, 1985. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  6. T. C. Sideris, B. Thomases, and D. Wang, “Long time behavior of solutions to the 3D compressible Euler equations with damping,” Communications in Partial Differential Equations, vol. 28, no. 3-4, pp. 795–816, 2003. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. Z. P. Xin, “Blowup of smooth solutions to the compressible Navier-Stokes equation with compact density,” Communications on Pure and Applied Mathematics, vol. 51, no. 3, pp. 229–240, 1998. View at Google Scholar
  8. T. Suzuki, “Irrotational blowup of the solution to compressible Euler equation,” Journal of Mathematical Fluid Mechanics, vol. 15, no. 3, pp. 617–633, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. Z. Lei, Y. Du, and Q. T. Zhang, “Singularities of solutions to compressible Euler equations with vacuum,” Mathematical Research Letters, vol. 20, no. 1, pp. 41–50, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  10. T. Li and D. Wang, “Blowup phenomena of solutions to the Euler equations for compressible fluid flow,” Journal of Differential Equations, vol. 221, no. 1, pp. 91–101, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. D. Li, C. X. Miao, and X. Y. Zhang, “On the isentropic compressible Euler equation with adiabatic index γ = 1,” Pacific Journal of Mathematics, vol. 262, no. 1, pp. 109–128, 2013. View at Publisher · View at Google Scholar