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Uniform stability of the interactive system of full Karman equation and viscous fluid equation

Banff International Research Station for Mathematical Innovation and Discovery

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.

Mathematics; Partial differential equations; Systems theory; control; Control/optimization/operation research

video/mp4

Author affiliation: Kharkiv National University

2018-01-15

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/64359

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/