Incompressible Navier–Stokes equations on a thin spherical domain \(Q_\varepsilon \) along with free boundary conditions under a random forcing are considered. The convergence of the martingale solution of these equations to the martingale solution of the stochastic Navier–Stokes equations on a sphere \(\mathbb {S}^2\) as the thickness converges to zero is established.

中文翻译：

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薄球域上的随机 Navier-Stokes 方程

考虑了薄球域\(Q_\varepsilon \)上的不可压缩 Navier-Stokes 方程以及随机强迫下的自由边界条件。当厚度收敛到零时，这些方程的鞅解与球体\(\mathbb {S}^2\)上的随机 Navier-Stokes 方程的鞅解的收敛成立。