Abstract
We prove existence on infinite time intervals of regular solutions to the 3D rotating Navier-Stokes equations in the limit of strong rotation (large Coriolis parameter Ω). This uniform existence is proven for periodic or stress-free boundary conditions for all domain aspect ratios, including the case of three wave resonances which yield nonlinear 2 1/2-dimensional limit equations; smoothness assumptions are the same as for local existence theorems. The global existence is proven using techniques of the Littlewood-Paley dyadic decomposition. Infinite time regularity for solutions of the 3D rotating Navier-Stokes equations is obtained by bootstrapping from global regularity of the limit equations and convergence theorems.
Original language | English (US) |
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Pages (from-to) | 51-57 |
Number of pages | 7 |
Journal | Applied Mathematics Letters |
Volume | 13 |
Issue number | 4 |
DOIs | |
State | Published - May 2000 |
Keywords
- Resonances
- Rotation
- Three-dimensional Navier-Strokes equations
ASJC Scopus subject areas
- Applied Mathematics