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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