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

Abstract

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. Insidethe 'vertical' pipe there is a heavy piston which can freely slide along the pipe. On the lateralboundary of the 'vertical' pipe we prescribe Navier's slip boundary conditions. We prove the existence ofa local in time weak solution. Furthermore, we show that the obtained solution is a strong solution.