Small data global existence for a fluid-structure model

Mihaela Ignatova; Igor Kukavica; Irena Lasiecka; Amjad Tuffaha

doi:10.1088/1361-6544/aa4ec4

Small data global existence for a fluid-structure model

Mihaela Ignatova, Igor Kukavica, Irena Lasiecka, Amjad Tuffaha

Mathematics

Research output: Contribution to journal › Article › peer-review

24 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 language	English (US)
Pages (from-to)	848-898
Number of pages	51
Journal	Nonlinearity
Volume	30
Issue number	2
DOIs	https://doi.org/10.1088/1361-6544/aa4ec4
State	Published - 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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10.1088/1361-6544/aa4ec4

Cite this

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title = "Small data global existence for a fluid-structure model",

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.",

keywords = "Navier-Stokes equations, damped wave equation, fluid-structure interaction, global solutions, long time behavior",

author = "Mihaela Ignatova and Igor Kukavica and Irena Lasiecka and Amjad Tuffaha",

note = "Funding Information: MI was supported in part by the NSF FRG grant DMS-115893, IK was supported in part by the NSF grants DMS-1311943 and DMS-1615239, IL was supported in part by the NSF grant DMS-0104305 and by the Air Force grant AFOSR9550-09-1-0459. Publisher Copyright: {\textcopyright} 2017 IOP Publishing Ltd & London Mathematical Society.",

year = "2017",

month = feb,

doi = "10.1088/1361-6544/aa4ec4",

language = "English (US)",

volume = "30",

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T1 - Small data global existence for a fluid-structure model

AU - Ignatova, Mihaela

AU - Kukavica, Igor

AU - Lasiecka, Irena

AU - Tuffaha, Amjad

N1 - Funding Information: MI was supported in part by the NSF FRG grant DMS-115893, IK was supported in part by the NSF grants DMS-1311943 and DMS-1615239, IL was supported in part by the NSF grant DMS-0104305 and by the Air Force grant AFOSR9550-09-1-0459. Publisher Copyright: © 2017 IOP Publishing Ltd & London Mathematical Society.

PY - 2017/2

Y1 - 2017/2

N2 - 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.

AB - 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.

KW - Navier-Stokes equations

KW - damped wave equation

KW - fluid-structure interaction

KW - global solutions

KW - long time behavior

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SN - 0951-7715

VL - 30

SP - 848

EP - 898

JO - Nonlinearity

JF - Nonlinearity

IS - 2

ER -

Small data global existence for a fluid-structure model

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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