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Theme for TIFR Centre For Applicable Mathematics, Bangalore

Abstract  :  In this talk, we discuss the stabilization of a fluid-structure interaction system of a viscous, compressible fluid and rigid ball in a three dimension space with an external force acting on the ball produced by a spring and a damper connecting the centre of the ball to a fixed point   $$h_1$$. We prove global-in-time existence result for this model under the condition that the initial velocities are small and the center of mass of the body is sufficiently near to $$h_1$$. In this scenario, we discuss the asymptotic behaviour of the whole system.