We study steady bifurcation for the coupled system body-liquid consisting of a sphere freely falling in a Navier-Stokes liquid under the action of gravity. In particular we show that, under the assumption that for the bifurcating solution the translational velocity of the sphere is parallel to the gravity, bifurcation takes place provided 1 is a simple eigenvalue of a suitable linear operator and the transversality property holds.

中文翻译：

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关于 Navier-Stokes 液体中落球稳定分岔的问题

我们研究了由在重力作用下自由落入 Navier-Stokes 液体中的球体组成的耦合系统体液的稳态分岔。特别地，我们表明，在假设对于分叉解球体的平移速度平行于重力的假设下，如果 1 是合适的线性算子的简单特征值并且横向性质成立，则会发生分叉。