On well-posedness and small data global existence for an interface damped free boundary fluid-structure model

Mihaela Ignatova; Igor Kukavica; Irena Lasiecka; Amjad Tuffaha

doi:10.1088/0951-7715/27/3/467

On well-posedness and small data global existence for an interface damped free boundary fluid-structure model

Mihaela Ignatova, Igor Kukavica, Irena Lasiecka, Amjad Tuffaha

Mathematics

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

54 Scopus citations

Abstract

We address a fluid-structure system which consists of the incompressible Navier-Stokes equations and a damped linear wave equation defined on two dynamic domains. The equations are coupled through transmission boundary conditions and additional boundary stabilization effects imposed on the free moving interface separating the two domains. Given sufficiently small initial data, we prove the global-in-time existence of solutions by establishing a key energy inequality which in addition provides exponential decay of solutions.

Original language	English (US)
Pages (from-to)	467-499
Number of pages	33
Journal	Nonlinearity
Volume	27
Issue number	3
DOIs	https://doi.org/10.1088/0951-7715/27/3/467
State	Published - Mar 2014

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics
General Physics and Astronomy
Applied Mathematics

Keywords

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

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10.1088/0951-7715/27/3/467

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abstract = "We address a fluid-structure system which consists of the incompressible Navier-Stokes equations and a damped linear wave equation defined on two dynamic domains. The equations are coupled through transmission boundary conditions and additional boundary stabilization effects imposed on the free moving interface separating the two domains. Given sufficiently small initial data, we prove the global-in-time existence of solutions by establishing a key energy inequality which in addition provides exponential decay of solutions.",

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AU - Ignatova, Mihaela

AU - Kukavica, Igor

AU - Lasiecka, Irena

AU - Tuffaha, Amjad

PY - 2014/3

Y1 - 2014/3

N2 - We address a fluid-structure system which consists of the incompressible Navier-Stokes equations and a damped linear wave equation defined on two dynamic domains. The equations are coupled through transmission boundary conditions and additional boundary stabilization effects imposed on the free moving interface separating the two domains. Given sufficiently small initial data, we prove the global-in-time existence of solutions by establishing a key energy inequality which in addition provides exponential decay of solutions.

AB - We address a fluid-structure system which consists of the incompressible Navier-Stokes equations and a damped linear wave equation defined on two dynamic domains. The equations are coupled through transmission boundary conditions and additional boundary stabilization effects imposed on the free moving interface separating the two domains. Given sufficiently small initial data, we prove the global-in-time existence of solutions by establishing a key energy inequality which in addition provides exponential decay of solutions.

KW - Navier-Stokes equations

KW - damped wave equation

KW - fluid-structure interaction

KW - global solutions

KW - long time behaviour

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VL - 27

SP - 467

EP - 499

JO - Nonlinearity

JF - Nonlinearity

IS - 3

ER -

On well-posedness and small data global existence for an interface damped free boundary fluid-structure model

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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