Communications in Mathematical Physics

, Volume 215, Issue 3, pp 559–581

On Spherically Symmetric Solutions¶of the Compressible Isentropic Navier–Stokes Equations

  • Song Jiang
  • Ping Zhang

DOI: 10.1007/PL00005543

Cite this article as:
Jiang, S. & Zhang, P. Commun. Math. Phys. (2001) 215: 559. doi:10.1007/PL00005543


We prove the global existence of weak solutions to the Cauchy problem for the compressible isentropic Navier–Stokes equations in ℝn (n= 2, 3) when the Cauchy data are spherically symmetric. The proof is based on the exploitation of the one-dimensional feature of symmetric solutions and use of a new (multidimensional) property induced by the viscous flux. The present paper extends Lions' existence theorem [15] to the case 1< γ <γn for spherically symmetric initial data, where γ is the specific heat ratio in the pressure, γn= 3/2 for n= 2 and γn= 9/5 for n= 3.

Dedicated to Professor Rolf Leis on the occasion of his 70th birthday

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Song Jiang
    • 1
  • Ping Zhang
    • 2
  1. 1.Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing 100088, P. R. China. E-mail:
  2. 2.Institute of Mathematics, Academia Sinica, Beijing 100080, P. R. China.¶E-mail:

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