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.

中文翻译：

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流体静力学 Navier-Stokes 方程的适定性

我们解决了流体静力 Navier-Stokes 方程的局部适定性。这些方程有时称为简化的 Navier-Stokes/Prandtl，在对纵横比和雷诺数的某些限制下，作为 Navier-Stokes 系统在薄域中的形式限制出现。众所周知，在对初始数据没有任何结构假设的情况下，实解析性对于系统的局部适定性既是必要的也是充分的。在本文中，我们证明了对于凸初始数据，局部适定性在简单的 Gevrey 正则性下成立。