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April  2012, 32(4): 1355-1389. doi: 10.3934/dcds.2012.32.1355

## Solutions to a fluid-structure interaction free boundary problem

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

Received  September 2010 Revised  June 2011 Published  October 2011

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 $H^{2}$.
Citation: Igor Kukavica, Amjad Tuffaha. Solutions to a fluid-structure interaction free boundary problem. Discrete & Continuous Dynamical Systems - A, 2012, 32 (4) : 1355-1389. doi: 10.3934/dcds.2012.32.1355
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