Advances in Differential Equations
- Adv. Differential Equations
- Volume 13, Number 9-10 (2008), 801-828.
On strong solutions of a planetary geostrophic model of the ocean
We study, in this article, the well-posedness of a planetary geostrophic (PG) model of the ocean. This model is derived from the PG studied in  by adding a (non-linear) advection term in the horizontal momentum equation. We address in particular the question of existence and uniqueness of global (in time) weak solution to the model. We also discuss the asymptotic behavior of the weak solutions and the stability of the stationary solutions. We prove that any weak solution to the model converges exponentially with time to a weak solution to the primitive equations of the ocean provided that the data are small.
Adv. Differential Equations Volume 13, Number 9-10 (2008), 801-828.
First available in Project Euclid: 18 December 2012
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 86A05: Hydrology, hydrography, oceanography [See also 76Bxx, 76E20, 76Q05, 76Rxx, 76U05]
Secondary: 35A05 76D03: Existence, uniqueness, and regularity theory [See also 35Q30] 76U05: Rotating fluids
Tachim Medjo, T. On strong solutions of a planetary geostrophic model of the ocean. Adv. Differential Equations 13 (2008), no. 9-10, 801--828. https://projecteuclid.org/euclid.ade/1355867320