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Note on evolutionary free piston problem for Stokes equations with slip boundary conditions

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  • In this paper we study a free boundary fluid-rigid body interaction problem, the free piston problem. We consider an evolutionary incompressible viscous fluid flow through a junction of two pipes. Inside the "vertical" pipe there is a heavy piston which can freely slide along the pipe. On the lateral boundary of the "vertical" pipe we prescribe Navier's slip boundary conditions. We prove the existence of a local in time weak solution. Furthermore, we show that the obtained solution is a strong solution.
    Mathematics Subject Classification: Primary: 74F10, 35Q30, 76D03; Secondary: 76D05.


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