Advances in Differential Equations

Derivation of quasi-geostrophic potential vorticity equations

B. Desjardins and E. Grenier

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In this paper we derive the quasi-geostrophic potential vorticity equations, starting from primitive type equations, as the Rossby number goes to zero, and prove the convergence as long as the limit system has strong enough solutions. We in particular take account of the boundary layers and investigate the existence of global weak solutions of the limit system with physical boundary conditions.

Article information

Adv. Differential Equations Volume 3, Number 5 (1998), 715-752.

First available in Project Euclid: 18 April 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 86A05: Hydrology, hydrography, oceanography [See also 76Bxx, 76E20, 76Q05, 76Rxx, 76U05] 35B25: Singular perturbations 76U05: Rotating fluids 76V05: Reaction effects in flows [See also 80A32] 86A10: Meteorology and atmospheric physics [See also 76Bxx, 76E20, 76N15, 76Q05, 76Rxx, 76U05]


Desjardins, B.; Grenier, E. Derivation of quasi-geostrophic potential vorticity equations. Adv. Differential Equations 3 (1998), no. 5, 715--752.

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