Solutions to a fluid-structure interaction free boundary problem

Igor Kukavica; Amjad Tuffaha

doi:10.3934/dcds.2012.32.1355

Article Contents

2012, Volume 32, Issue 4: 1355-1389. Doi: 10.3934/dcds.2012.32.1355

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Solutions to a fluid-structure interaction free boundary problem

Igor Kukavica^1, and
Amjad Tuffaha^2,

1.
Department of Mathematics, University of Southern California, Los Angeles, CA 90089
2.
Department of Mathematics, The Petroleum Institute, Abu Dhabi

Received: August 31, 2010

Revised: May 31, 2011

Published: March 2012

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Abstract

Our main result is the existence of solutions to the free boundary fluid-structure interaction system. The system consists of a Navier-Stokes equation and a wave equation defined in two different but adjacent domains. The interaction is captured by stress and velocity matching conditions on the free moving boundary lying in between the two domains. We prove the local existence of a solution when the initial velocity of the fluid belongs to $H^{3}$ while the velocity of the elastic body is in $H^{2}$.

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Mathematics Subject Classification: Primary: 35Q30, 74F10, 76D05; Secondary: 35K15, 35K55, 35M30.

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