On the hydrostatic Navier–Stokes equations with Gevrey class 2 data

In this paper, we study the two-dimensional hydrostatic Navier–Stokes equations in the strip domain \({\mathbb R}\times \mathbb {T}\) $\mathbb{R}\times \mathbb{T}$ . Motivated by Gérard-Varet et al. (Anal PDE 13(5):1417–1455 2020), we obtain the local well-posedness result in Gevrey class 2 when the initial data is a small perturbation of some convex function. Then we justify strictly the limit from the anisotropic Navier–Stokes system to the hydrostatic Navier–Stokes system.