ON THE REGULARITY OF THREE-DIMENSIONAL ROTATING EULER–BOUSSINESQ EQUATIONS

Author:

BABIN A.12,MAHALOV A.3,NICOLAENKO B.3

Affiliation:

1. Department of Mathematics, University of California, Irvine, CA 92717, USA

2. MIIT, Moscow, Obrazcova 15, Russia

3. Department of Mathematics, Arizona State University, Tempe, AZ 85287, USA

Abstract

The 3-D rotating Boussinesq equations (the "primitive" equations of geophysical fluid flows) are analyzed in the asymptotic limit of strong stable stratification. The resolution of resonances and a nonstandard small divisor problem are the basis for error estimates for such fast singular oscillating limits. Existence on infinite time intervals of regular solutions to the viscous 3-D "primitive" equations is proven for initial data in Hα, α≥ 3/4. Existence on a long-time interval T*of regular solutions to the 3-D inviscid equations is proven for initial data in Hα, α > 5/2 (T*→∞ as the frequency of gravity waves →∞).

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modeling and Simulation

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