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

#### 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.

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