Conditionally strong solution for macroscopic polymeric SSS interaction

TL;DR

This paper proves the existence of a unique global strong solution for a complex fluid-structure interaction model involving Oldroyd-B fluids and viscoelastic shells, under specific regularity conditions.

Contribution

It establishes a conditional strong solution existence result for a coupled polymeric fluid and viscoelastic shell system, relaxing previous constraints on certain variables.

Findings

Existence of a unique global strong solution under Ladyzhenskaya--Prodi--Serrin condition.

No need for polymer number density or extra stress tensor regularity.

Solution persists globally in time with bounded shell displacement.

Abstract

The system under study is a solute-solvent-structure (SSS) interaction problem for the interaction of a dilute three-dimensional Oldroyd-B polymeric fluid with a two-dimensional viscoelastic shell. We show that a unique global strong solution to this system exists under the condition that the classical Ladyzhenskaya--Prodi--Serrin criterion holds for the velocity field and that the shell displacement is essentially bounded in time with values in the space of continuously differentiable functions. No requirement is needed for the polymer number density and the extra stress tensor for the solute component.