Mathematical Analysis and Optimal Control Problems for the Perturbation of the Primitive Equations of the Ocean with Vertical Viscosity
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A. Belmiloudi
Abstract
In this paper we consider an oceanic domain in ℝ3, in which there exists, at initial time, a current U0, a pressure p0 and a density ρ0. The perturbation U, p and ρ of the velocity, the pressure and the density are induced by a perturbation of the mean windstress. The equations are of Navier-Stokes type for the velocity and pressure, of transport-diffusion type for the density. They are linearized around a given mean circulation and modified by the physical assumptions including the Boussinesq approximation and the Hydrostatic approximation with vertical viscosity. The existence and uniqueness of the solution for the variational problem are studied for the three-dimensional problem, and for the two-dimensional cyclic problem derived by assuming a sinusoidal x-dependence for the perturbation of mean flow. The latter corresponds to a modelization of tropical instability waves which are illustrated by El Nino phenomenon.
© Heldermann Verlag
Articles in the same Issue
- Mathematical Analysis and Optimal Control Problems for the Perturbation of the Primitive Equations of the Ocean with Vertical Viscosity
- On Density Topologies with Respect to Invariant σ-Ideals
- Singularly Perturbed Systems of Volterra Equations
- Nonlocal in Time Problems for Evolution Equations of Second Order
- Oscillation of Solutions to Nonlinear Neutral Delay Differential Equations
- On the Order Structure of Time Projection
- Hukuhara's Derivative and Concave Iteration Semigroups of Linear Set-Valued Functions
Articles in the same Issue
- Mathematical Analysis and Optimal Control Problems for the Perturbation of the Primitive Equations of the Ocean with Vertical Viscosity
- On Density Topologies with Respect to Invariant σ-Ideals
- Singularly Perturbed Systems of Volterra Equations
- Nonlocal in Time Problems for Evolution Equations of Second Order
- Oscillation of Solutions to Nonlinear Neutral Delay Differential Equations
- On the Order Structure of Time Projection
- Hukuhara's Derivative and Concave Iteration Semigroups of Linear Set-Valued Functions
