| Issue |
ESAIM: M2AN
Volume 34, Number 2, March/April 2000
Special issue for R. Teman's 60th birthday
|
|
|---|---|---|
| Page(s) | 201 - 222 | |
| DOI | https://doi.org/10.1051/m2an:2000138 | |
| Published online | 15 April 2002 | |
Fast Singular Oscillating Limits and Global Regularity for the 3D Primitive Equations of Geophysics
1
Department of Mathematics, University of California, Irvine, CA, 92697, USA.
2
Department of Mathematics, Arizona State University, Tempe, AZ 85287, USA.
Received:
15
November
1999
Fast singular oscillating limits of
the three-dimensional "primitive" equations of
geophysical fluid flows are analyzed.
We 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
for all domain aspect ratios,
including the case of three wave resonances
which yield nonlinear "
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.
Mathematics Subject Classification: 76D05 / 76D50 / 76U05 / 86A10
Key words: Fast singular oscillating limits / three-dimensional Navier-Stokes equations / primitive equations for geophysical fluid flows.
© EDP Sciences, SMAI, 2000
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