## Abstract

In this paper, we analyze a tamed 3D Navier-Stokes equation in uniform C^{2}-domains (not necessarily bounded), which obeys the scaling invariance principle, and prove the existence and uniqueness of strong solutions to this tamed equation. In particular, if there exists a bounded solution to the classical 3D Navier-Stokes equation, then this solution satisfies our tamed equation. Moreover, the existence of a global attractor for the tamed equation in bounded domains is also proved. As a simple application, we obtain that the set of all initial values for which the classical Navier-Stokes equation admits a bounded strong solution is open in H^{2}.

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

Pages (from-to) | 3093-3112 |

Number of pages | 20 |

Journal | Nonlinear Analysis, Theory, Methods and Applications |

Volume | 71 |

Issue number | 7-8 |

DOIs | |

Publication status | Published - 1 Oct 2009 |

Externally published | Yes |

## Keywords

- Global attractor
- Navier-Stokes equation
- Strong solution

## Fingerprint

Dive into the research topics of 'A tamed 3D Navier-Stokes equation in uniform C^{2}-domains'. Together they form a unique fingerprint.