### Abstract

We prove the global existence of weak solutions of the Navier-Stokes equations of compressible, nonbarotropic flow in three space dimensions with initial data and external forces which are large, discontinuous, and spherically or cylindrically symmetric. The analysis allows for the possibility that a vacuum state emerges at the origin or axis of symmetry, and the equations hold in the sense of distributions in the set where the density is positive. In addition, the mass and momentum equations hold weakly in the entire space-time domain, but with a nonstandard interpretation of the viscosity terms as distributions. Solutions are obtained as limits of solutions in annular regions between two balls or cylinders, and the analysis allows for the possibility that energy is absorbed into the origin or axis, and is lost in the limit as the inner radius goes to zero.

Original language | English (US) |
---|---|

Pages (from-to) | 297-343 |

Number of pages | 47 |

Journal | Archive for Rational Mechanics and Analysis |

Volume | 173 |

Issue number | 3 |

DOIs | |

State | Published - Sep 1 2004 |

### All Science Journal Classification (ASJC) codes

- Analysis
- Mathematics (miscellaneous)
- Mechanical Engineering