Global existence of weak solutions for viscous incompressible flows around a moving rigid body in three dimensions. (English) Zbl 0970.35096

The authors consider a coupled system of nonlinear partial and ordinary differential equations modeling the motion of a rigid body of arbitrary shape immersed in a fluid flow in a bounded, three-dimensional domain. The motion of the body is caused by the action of given forces exerted on the fluid and on the rigid body. The governing equations for the fluid flow are given by the classical Navier-Stokes system whereas the motion of the solid is governed by the equations for the balance of linear and nonlinear angular momentum. For this problem, the global existence of weak solutions is proven.


35Q30 Navier-Stokes equations
35D05 Existence of generalized solutions of PDE (MSC2000)
76D05 Navier-Stokes equations for incompressible viscous fluids
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