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BIRS Workshop Lecture Videos

Uniform stability of the interactive system of full Karman equation and viscous fluid equation Ryzhkova-Gerasymova, Iryna


We study well-posedness and asymptotic dynamics of a coupled system consisting of linearized 3D Navier--Stokes equations in a bounded domain and a classical (nonlinear) full von Karman plate equations that accounts for both transversal and lateral displacements on a flexible part of the boundary. Rotational inertia of filaments of the shell is not taken into account. We also do not assume any mechanical damping acting on the palte equations. Our main result shows well-posedness of strong solutions to the problem, thus the problem generates a semiflow in an appropriate phase space. We also prove uniform stability of strong solutions to homogeneous problem in the norm of strong phase space. Thus, viscous energy dissipation in the fluid component is sufficient to stabilize the whole system plate+fluid.

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