IUMJ

Title: Solutions to a free boundary problem of fluid-structure interaction

Authors: Igor Kukavica and Amjad Tuffaha

Issue: Volume 61 (2012), Issue 5, 1817-1859

Abstract:

We establish new \emph{a priori} estimates for existence and uniqueness of smooth solutions to the free boundary fluid-structure interaction system treated previously in [D. Coutand and S. Shkoller, \textit{Motion of an elastic solid inside an incompressible viscous fluid}, Arch. Ration. Mech. Anal. \textbf{176} (2005), no. 1, 25--102], [I. Kukavica and A. Tuffaha, \textit{Solutions to a fluid-structure interaction free boundary problem}, Discrete Contin. Dyn. Syst. \textbf{32} (2012), no. 4, 1355--1389]. Unlike [I. Kukavica and A. Tuffaha, \textit{Solutions to a fluid-structure interaction free boundary problem}, Discrete Contin. Dyn. Syst. \textbf{32} (2012), no. 4, 1355--1389], we perform the analysis on a domain with a nonflat boundary, which requires a change for the space of initial data and the space for solutions. The existence result covers a range of exponents where there is no loss of smoothness in solutions to the hyperbolic elastic equations capturing elastic body motion. Moreover, the spaces needed for existence and uniqueness enlarge the previously known spaces of initial data.