Small data global existence for a fluid-structure model

Mihaela Ignatova, Igor Kukavica, Irena Lasiecka, Amjad Tuffaha

Research output: Contribution to journalArticle

11 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)848-898
Number of pages51
JournalNonlinearity
Volume30
Issue number2
DOIs
StatePublished - Feb 2017

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

Keywords

  • Navier-Stokes equations
  • damped wave equation
  • fluid-structure interaction
  • global solutions
  • long time behavior

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  • Cite this

    Ignatova, M., Kukavica, I., Lasiecka, I., & Tuffaha, A. (2017). Small data global existence for a fluid-structure model. Nonlinearity, 30(2), 848-898. https://doi.org/10.1088/1361-6544/aa4ec4