Local well-posedness of the equations governing the motion of a fluid-filled elastic solid

2025/06/28 by Giusy Mazzone, Mazzone, Giusy
Engineering · Mathematics · #35K61 #35L20 #35Q35 #74B05 #74B10 #76D05 #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations #Thermoelastic and Magnetoelastic Phenomena

paper · pdf · doi:10.48550/arxiv.2506.22874

openalex publication_date 2025/06/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the fluid-structure interaction problem of a viscous incompressible fluid contained in an elastic solid whose motion is not prescribed. The equations governing the motion of the solid are given by the Navier equations of linear elasticity, whereas the fluid motion is described by the Navier-Stokes equations. We prove that the governing equations admit a unique strong solution corresponding to non-zero initial data for the solid initial displacement and velocity, and for a fluid initial velocity in H^5/2.

Citations

• On a model of an elastic body fully immersed in a viscous incompressible fluid with small data
• Global well-posedness and exponential decay for a fluid-structure model with small data
• On the free rotations of rigid bodies with a liquid-filled gap
• On the free rotations of rigid bodies with a liquid-filled gap
• On the motion of a fluid-filled rigid body with Navier Boundary conditions
• Inertial Motions of a Rigid Body with a cavity filled with a viscous\n liquid
• Interpolation, embeddings and traces of anisotropic fractional Sobolev\n spaces with temporal weights

Related

• On the local existence of solutions to the fluid-structure interaction problem with a free interface
• On the local existence of solutions to the fluid-structure interaction problem with a free interface
• Smooth solutions for motion of a rigid body of general form in an incompressible perfect fluid
• Analysis of the interaction between an incompressible fluid and a quasi-incompressible non-linear elastic structure
• Local existence of Strong solutions for a fluid-structure interaction model