# 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}, author={Pascal Az{\'e}rad and Francisco Guill{\'e}n}, journal={SIAM J. Math. Anal.}, year={2001}, volume={33}, pages={847-859} }

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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