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On the Zero-Rossby Limit for the Primitive Equations of Atmosphere

#### Author: Gui-Qiang Chen and Ping Zhang

#### Title:
On the Zero-Rossby Limit for the Primitive Equations of Atmosphere

**Abstract**
The zero-Rossby limit for the primitive equations (PE) governing
the atmospheric motions is analyzed.
The limit is important in geophysics for large scale models
(cf. Lions 1996, ICIAM 95 (Hamburg 1995) (Math. Res. vol. 87)
(Berlin: Akademie) pp. 177-212) and is in the level of the zero relaxation
limit for nonlinear partial differential equations (cf.
Chen, Levermore, and Liu 1994, Comm. Pure Appl. Math. 47, 787-830).
It is proved that, if the initial data appropriately approximate
data of geostrophic type,
the corresponding solutions of the simplified primitive equations
approximate the solutions of the quasigeostrophic equations (QG)
with order $\ep$ accuracy as the Rossby number $\ep$ goes to zero.

This article has appeared in:

*Nonlinearity*,
**14**, pages 1279-1295 (2001)

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A closely related paper is Change me.

**Author Address**
Department of Mathematics
Northwestern University
Evanston, IL 60208-2730
gqchen@math.nwu.edu