# Mathematical Justification of the Hydrostatic Approximation in the Primitive Equations of Geophysical Fluid Dynamics

@article{Azrad2001MathematicalJO,
title={Mathematical Justification of the Hydrostatic Approximation in the Primitive Equations of Geophysical Fluid Dynamics},
journal={SIAM J. Math. Anal.},
year={2001},
volume={33},
pages={847-859}
}
• Published 2001
• Geology, Mathematics
• SIAM J. Math. Anal.
Geophysical fluids all exhibit a common feature: their aspect ratio (depth to hori- zontal width) is very small. This leads to an asymptotic model widely used in meteorology, oceanog- raphy, and limnology, namely the hydrostatic approximation of the time-dependent incompressible Navier-Stokes equations. It relies on the hypothesis that pressure increases linearly in the vertical direction. In the following, we prove a convergence and existence theorem for this model by means of anisotropic…
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