Archive for Rational Mechanics and Analysis

, Volume 177, Issue 3, pp 479–511

The Lifespan of a Class of Smooth Spherically Symmetric Solutions of the Compressible Euler Equations with Variable Entropy in Three Space Dimensions


DOI: 10.1007/s00205-005-0374-5

Cite this article as:
Godin, P. Arch. Rational Mech. Anal. (2005) 177: 479. doi:10.1007/s00205-005-0374-5


We consider smooth three-dimensional spherically symmetric Eulerian flows of ideal polytropic gases with variable entropy, whose initial data are obtained by adding a small smooth perturbation with compact support to a constant state. Under a natural assumption, we obtain precise information on the asymptotic behavior of their lifespan when the size of the initial perturbation tends to 0. This is achieved by the construction and estimate of a suitable approximate flow.

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.Département de MathématiquesUniversité Libre de BruxellesBoulevard duTriompheBelgium