On the hydrostatic and Darcy limits of the convective Navier-Stokes equations

Abstract

The author studies two singular limits of the convective Navier-Stokes equations. The hydrostatic limit is first studied: the author shows the existence of global solutions with a convex pressure field and derives them from the convective Navier-Stokes equations as long as the pressure field is smooth and strongly convex. The (friction dominated) Darcy limit is also considered, and a relaxed version is studied.

Keywords

Atmospheric sciences / Fluid mechanics / Asymptotic analysis

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