### Abstract

We study the 3-D compressible Navier-Stokes equations with an external potential force and a general non-decreasing pressure. We prove the global-in-time existence of weak solutions with small-energy initial data and with densities being non-negative and essentially bounded. A solution may have large oscillations and contain vacuum states. No smallness assumption is made on the external force nor the initial perturbation in L∞ for density. Initial velocity u₀ is taken to be bounded in Lq for some q > 6 and no further regularity assumption is imposed on u₀. Finally, we discuss the uniqueness of weak solutions. Copyright
© 2016 AIP Publishing.

Original language | English |
---|---|

Article number | 081513 |

Journal | Journal of Mathematical Physics |

Volume | 57 |

Issue number | 8 |

Early online date | Aug 2016 |

DOIs | |

Publication status | Published - 2016 |

### Fingerprint

Compressible Navier-Stokes Equations

uniqueness

Navier-Stokes equation

Weak Solution

Existence and Uniqueness

Existence of Weak Solutions

Energy

regularity

3D

Vacuum

Uniqueness

Regularity

Non-negative

Oscillation

Perturbation

perturbation

vacuum

oscillations

energy