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On a motion of a solid body in a viscous fluid. Two-dimensional case. (English) Zbl 0966.76016

Summary: We investigate the two-dimensional problem on the motion of a rigid a body in bounded container filled by viscous fluid. The main assumption making possible to prove the global existence of a generalized solution is that the boundaries of the body and container are curves of the class \(C^2\). We show that in this case the body impacts on the wall with zero velocity, and does not move during the touching.

MSC:

76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
76D05 Navier-Stokes equations for incompressible viscous fluids
70E99 Dynamics of a rigid body and of multibody systems
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