Small data global existence for a fluid-structure model

We address the system of partial differential equations modeling motion of an elastic body inside an incompressible fluid. The fluid is modeled by the incompressible Navier-Stokes equations while the structure is represented by the damped wave equation with interior damping. The additional boundary...

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Bibliographic Details
Published in:Nonlinearity 2017-02, Vol.30 (2), p.848-898
Main Authors: Ignatova, Mihaela, Kukavica, Igor, Lasiecka, Irena, Tuffaha, Amjad
Format: Article
Language:English
Subjects:
damped wave equation
fluid-structure interaction
global solutions
long time behavior
Navier-Stokes equations
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Summary:We address the system of partial differential equations modeling motion of an elastic body inside an incompressible fluid. The fluid is modeled by the incompressible Navier-Stokes equations while the structure is represented by the damped wave equation with interior damping. The additional boundary stabilization γ, considered in our previous paper, is no longer necessary. We prove the global existence and exponential decay of solutions for small initial data in a suitable Sobolev space.
ISSN:0951-7715
1361-6544
DOI:10.1088/1361-6544/aa4ec4