## Abstract

Fast singular oscillating limits of the three-dimensional "primitive" equations of geophysical fluid flows are analyzed. VVe prove existence on infinite time intervals of regular solutions to the 3D "primitive" Navier-Stokes equations for strong stratification (large stratification parameter N). This uniform existence is proven for periodic or stress-free boundary conditions tor all domain aspect ratios, including the case of three wave resonances which yield nonlinear "21/2 dimensional" limit equations for N → +∞; smoothness assumptions are the same as for local existence theorems, that is initial data in Hα, α ≥ 3/4. The global existence is proven using techniques of the Littlewood-Paley dyadic decomposition. Infinite time regularity for solutions of the 3D "primitive" Navier-Stokes equations is obtained by bootstrapping from global regularity of the limit resonant equations and convergence theorems.

Original language | English (US) |
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Pages (from-to) | 201-222 |

Number of pages | 22 |

Journal | Mathematical Modelling and Numerical Analysis |

Volume | 34 |

Issue number | 2 |

DOIs | |

State | Published - 2000 |

## Keywords

- Fast singular oscillating limits
- Primitive equations for geophysical fluid flows
- Three-dimensional Navier-Stokes equations

## ASJC Scopus subject areas

- Analysis
- Numerical Analysis
- Modeling and Simulation
- Computational Mathematics
- Applied Mathematics