Backward Uniqueness for a PDE Fluid-Structure Interaction

TL;DR

This paper proves the backward uniqueness property for a coupled PDE system modeling fluid-structure interaction, involving 3D Stokes flow and a 2D plate, through resolvent estimates of the semigroup generator.

Contribution

It establishes backward uniqueness for a fluid-structure PDE system, a novel result in the analysis of coupled PDE models in fluid mechanics.

Findings

Backward uniqueness property proven for the PDE system.

Resolvent estimates for the semigroup generator obtained.

Advances understanding of PDE behavior in fluid-structure interactions.

Abstract

In this work, we establish the so-called backward uniqiueness property for a coupled system of partial differential equations (PDEs) which governs a certain fluid-structure interaction. In particular, a three-dimensional Stokes flow interacts across a boundary interface with a two-dimensional mechanical plate equation. By way of attaining this result, a certain estimate is obtained for the associated semigroup generator resolvent.