Small-time solvability of primitive equations for the ocean with spatially-varying vertical mixing

Honda, Hirotada

ESAIM: Mathematical Modelling and Numerical Analysis , Tome 49 (2015) no. 3, pp. 875-919.

The small-time existence of a strong solution to the free surface problem of primitive equations for the ocean with variable turbulent viscosity terms is shown in this paper. In this model, the turbulent viscosity coefficients, which include the Richardson number depending on unknown variables, are explicitly formulated. In addition, following the formulation of practical models, the kinematic condition is assumed on the free ocean surface. As in preceding works, we consider the problem in the three-dimensional strip-like region, and assume the $f$-approximation. Under some conditions on the initial and boundary data and the topography of the bottom of the ocean, we construct a strong local-in-time solution in Sobolev–Slobodetskiĭ spaces. The boundedness of the temperature and salinity is also shown in the present paper.

Classification : 35M10, 35Q35, 35R35
Mots clés : Primitive equations, Sobolev–Slobodetskiĭ space, strong solution

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