We address the local well-posedness of the
hydrostatic Navier–Stokes equations.
These equations, sometimes called
reduced Navier–Stokes/Prandtl, appear as a formal
limit of the Navier–Stokes system in thin domains, under certain constraints on
the aspect ratio and the Reynolds number. It is known that without any
structural assumption on the initial data, real-analyticity is both necessary and
sufficient for the local well-posedness of the system. In this paper we prove
that for convex initial data, local well-posedness holds under simple Gevrey
regularity.
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