On the local existence of solutions to the fluid-structure interaction problem with a free interface

Abstract

We address a system of equations modeling an incompressible fluid interacting with an elastic body. We prove the local existence when the initial velocity belongs to the space $H^{1.5+\epsilon }$ and the initial structure velocity is in $H^{1+\epsilon }$, where $\epsilon \in (0,1/20)$.

arXiv comment22 pages. arXiv admin note: substantial text overlap with arXiv:2104.13500

References in corpus (3)

• On the motion of an elastic solid inside of an incompressible viscous fluid
• On the interaction between quasilinear elastodynamics and the Navier-Stokes equations
• Existence of a weak solution to a nonlinear fluid-structure interaction problem modeling the flow of an incompressible, viscous fluid in a cylinder with deformable walls