We investigate the existence and regularity of solutions to the stationary Stokes system and non-stationary Navier–Stokes equations in three dimensional bounded domains with in- and out-lets. We assume that on the in- and out-flow parts of the boundary the pressure is prescribed and the tangential component of the velocity field is zero, whereas on the lateral part of the boundary the fluid is at rest.

中文翻译：

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斯托克斯系统的流入和流出问题

我们研究带有入口和出口的三维有界域中固定Stokes系统和非平稳Navier-Stokes方程解的存在性和规律性。我们假设在边界的流入和流出部分规定了压力，速度场的切向分量为零，而在边界的侧面部分流体处于静止状态。