Some mathematical properties of the planetary geostrophic equations for large-scale ocean circulation

Abstract

We study in this article the well-posdness of the planetary geostrophic equations of the gyre-scale midlatitude ocean, and address in particular the question of the existence and some properties of global (in time) weak solutions of the planetary geostrophic equations of the gyre-scale midlatitude ocean. The main objective is to study effects of different friction and diffusion terms and to propose and to analyze proper boundary conditions for the correspondi models. Several open questions are also indicated.

Keywords:

• Planetary scale ocean dynamics
• planetary geostrophic equations
• primitive equation
• boundary effects
• 4th order diffusions
• existence and properties of solutions

¹College of Oceanic and Atmospheric Sciences, Oregon State University, 104 Ocean Admin. Bldg, Corvallis,OR 97331-5503, USA.

²Department of Mathematics and Institute for Scientific Computing & Applied Mathematics, Indiana University, Rawles Hall, Bloomington, IN 47405-5701, USA.

³Laboratoire d'Analyse Numerique, Universite Paris Sud, Batiment 425, 91405 Orsay, France.

¹College of Oceanic and Atmospheric Sciences, Oregon State University, 104 Ocean Admin. Bldg, Corvallis,OR 97331-5503, USA.

²Department of Mathematics and Institute for Scientific Computing & Applied Mathematics, Indiana University, Rawles Hall, Bloomington, IN 47405-5701, USA.

³Laboratoire d'Analyse Numerique, Universite Paris Sud, Batiment 425, 91405 Orsay, France.

Notes

¹College of Oceanic and Atmospheric Sciences, Oregon State University, 104 Ocean Admin. Bldg, Corvallis,OR 97331-5503, USA.

²Department of Mathematics and Institute for Scientific Computing & Applied Mathematics, Indiana University, Rawles Hall, Bloomington, IN 47405-5701, USA.

³Laboratoire d'Analyse Numerique, Universite Paris Sud, Batiment 425, 91405 Orsay, France.