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Nonuniqueness of a solution to the problem on motion of a rigid body in a viscous incompressible fluid. (English) Zbl 1148.35347

J. Math. Sci., New York 130, No. 4, 4893-4898 (2005); and Zap. Nauchn. Semin. POMI 306, 199-209 (2003).
Summary: This paper is devoted to the problem on motion of a rigid body in a viscous incompressible fluid. It is proved that there exist at least two weak solutions of this problem if collisions of the body with the boundary of the flow domain are allowed. These solutions describe different behavior of the body after the collision. Namely, for the first solution, the body goes away from the boundary after the collision. For the second solution, the body and the boundary remain in contact.

MSC:

35Q35 PDEs in connection with fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
70E15 Free motion of a rigid body
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