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) |
---|---|
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