On an attractor for strong solutions to interactive fluid-plate system without rotational inertia

2023/07/20 by Iryna Ryzhkova, Ryzhkova, Iryna
Computer Science · Engineering · Mathematics · #35B41 (Primary) #35Q30 #74F10 #74K20 #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Nonlinear Dynamics and Pattern Formation #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2307.11262

openalex publication_date 2023/07/20 · openalex created_date 2023/07/25 · openalex updated_date 2026/07/28

Abstract

We study long-time dynamics of strong solutions to a non-homogeneous coupled system consisting of linearized 3D Navier--Stokes equations in a bounded domain and the classical (nonlinear) full von Karman plate equations that account for both transversal and lateral displacements on a flexible part of the boundary. Rotational inertia of the filaments of the plate is not taken into account. Our main result is the existence of an attractor in the strong phase space provided lateral external loads are small enough.

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