# Fast Singular Oscillating Limits and Global Regularity for the 3D Primitive Equations of Geophysics

Anatoli Babin; Alex Mahalov; Basil Nicolaenko

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- Volume: 34, Issue: 2, page 201-222
- ISSN: 0764-583X

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topBabin, Anatoli, Mahalov, Alex, and Nicolaenko, Basil. "Fast Singular Oscillating Limits and Global Regularity for the 3D Primitive Equations of Geophysics." ESAIM: Mathematical Modelling and Numerical Analysis 34.2 (2010): 201-222. <http://eudml.org/doc/197472>.

@article{Babin2010,

abstract = {
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 "$2\frac\{1\}\{2\}$ 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.
},

author = {Babin, Anatoli, Mahalov, Alex, Nicolaenko, Basil},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Fast singular oscillating limits; three-dimensional Navier-Stokes equations;
primitive equations for geophysical fluid flows.; three-dimensional primitive equations; primitive Navier-Stokes equations; infinite time regularity; fast singular oscillating limits; geophysical flows; infinite time intervals; regular solutions; strong stratification; global existence; Littlewood-Paley dyadic decomposition; limit resonance equations; convergence},

language = {eng},

month = {3},

number = {2},

pages = {201-222},

publisher = {EDP Sciences},

title = {Fast Singular Oscillating Limits and Global Regularity for the 3D Primitive Equations of Geophysics},

url = {http://eudml.org/doc/197472},

volume = {34},

year = {2010},

}

TY - JOUR

AU - Babin, Anatoli

AU - Mahalov, Alex

AU - Nicolaenko, Basil

TI - Fast Singular Oscillating Limits and Global Regularity for the 3D Primitive Equations of Geophysics

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2010/3//

PB - EDP Sciences

VL - 34

IS - 2

SP - 201

EP - 222

AB -
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 "$2\frac{1}{2}$ 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.

LA - eng

KW - Fast singular oscillating limits; three-dimensional Navier-Stokes equations;
primitive equations for geophysical fluid flows.; three-dimensional primitive equations; primitive Navier-Stokes equations; infinite time regularity; fast singular oscillating limits; geophysical flows; infinite time intervals; regular solutions; strong stratification; global existence; Littlewood-Paley dyadic decomposition; limit resonance equations; convergence

UR - http://eudml.org/doc/197472

ER -

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