Time-periodic weak solutions for the interaction of an incompressible fluid with a linear Koiter type shell under dynamic pressure boundary conditions

2023/03/23 by Claudiu Mîndrilă, Mîndrilă, Claudiu, Sebastian Schwarzacher +1 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2303.13625

openalex publication_date 2023/03/23 · openalex created_date 2023/03/31 · openalex updated_date 2026/07/28

Abstract

In many occurrences of fluid-structure interaction time-periodic motions are observed. We consider the interaction between a fluid driven by the three dimensional Navier-Stokes equation and a two dimensional linearized elastic Koiter shell situated at the boundary. The fluid-domain is a part of the solution and as such changing in time periodically. On a steady part of the boundary we allow for the physically relevant case of dynamic pressure boundary values, prominent to model inflow/outflow. We provide the existence of at least one weak time-periodic solution for given periodic external forces that are not too large. For that we introduce new approximation techniques and a-priori estimates.

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• Strong time-periodic solutions to a multilayered fluid-structure interaction problem

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