Global well-posedness and exponential decay for a fluid-structure model with small data

2021/10/28 by Igor Kukavica, Wojciech S. Ożański, Kukavica, Igor +1 · 4 citations
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.2110.15284

openalex publication_date 2021/10/28 · openalex created_date 2022/08/31 · openalex updated_date 2026/08/01

Abstract

We address the system of partial differential equations modeling motion of an elastic body interacting with an incompressible fluid. The fluid is modeled by the incompressible Navier-Stokes equations while the structure is represented by a damped wave equation w_tt-Δw + αw_t =0, where α>0. We prove the global existence and exponential decay of strong solutions for small initial data in a suitable Sobolev space. We show that the elastic velocity w_t and the acceleration w_tt can be controlled by the H² elliptic estimates and by the dissipation of the fluid via the free interface. We also find that, even though the vanishing of the final displacement w appears invisible in the energy method, it can be deduced from the preservation of total volume. Our approach allows for any superlinear perturbation of the wave equation.

Cited by

• Exponential Decay of Solutions to a Fluid-Plate Model with Small Initial Data
• A global existence result on weak solutions for the 3D Navier-Stokes-plate system with no contact
• Strong stability and the Schiffer Conjecture for the fluid-elastic semigroup
• Local well-posedness of the equations governing the motion of a fluid-filled elastic solid

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