Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

Solutions to a fluid-structure interaction free boundary problem

Pages: 1355 - 1389, Volume 32, Issue 4, April 2012      doi:10.3934/dcds.2012.32.1355

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Igor Kukavica - Department of Mathematics, University of Southern California, Los Angeles, CA 90089, United States (email)
Amjad Tuffaha - Department of Mathematics, The Petroleum Institute, Abu Dhabi, United Arab Emirates (email)

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 $H^{2}$.

Keywords:  Fluid-structure interaction, Navier-Stokes equations, incompressible fluids.
Mathematics Subject Classification:  Primary: 35Q30, 74F10, 76D05; Secondary: 35K15, 35K55, 35M30.

Received: September 2010;      Revised: June 2011;      Available Online: October 2011.