Volume 8, Number 2, Summer 2000
ASYMPTOTIC BEHAVIOR OF THE PERTURBATION OF THE PRIMITIVE EQUATIONS OF THE OCEAN WITH VERTICAL VISCOSITY
AZIZ BELMILOUDI
Abstract. In this paper we consider an oceanic domain
included in R^{3} in which there exist, at initial time, a current
U0, a pressure p0 and a density ρ0. The perturbations
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 NavierStokes type for the velocity and pressure,
of transportdiffusion type for the density. They are modified
by the physical assumptions including the Boussinesq
approximation and the hydrostatic approximation with vertical
viscosity. The existence of the solution for the variational
problem is studied. We prove some results about the regularity
and then deduce the uniqueness. This result is valid in a
domain Ω with corners. It is proved by means of an extension
method, with evenodd reflection. In order to study the
asymptotic behavior of the perturbation, we introduce some
operators and give some properties for these operators. Under
some assumptions, we prove that the perturbation tends
to 0 as t tends to +∞ and that the solution of the variational
problem is a strong solution for every time t in [0,+∞ ].
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