## Existence of solutions for the equations modelling the motion of a rigid body in a viscous fluid.(English)Zbl 0954.35135

The motion of a rigid body inside a fluid flow (given by Navier-Stokes equations) is considered. The form of the fluid domain depends on the solutions, then a free boundary problem is considered, in a non-cylindrical domain of $$\mathbb{R}^3$$. The existence of local weak solutions of the penalized problem is proved. By passing to the limit in this last problem, the existence of at least one weak solution for the initial problem is shown. In a special case, the result is global in time. Some very interesting a priori estimates are given and the Faedo-Galerkin method is used.

### MSC:

 35Q35 PDEs in connection with fluid mechanics 35D05 Existence of generalized solutions of PDE (MSC2000) 76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
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### References:

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