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Existence of global weak solutions for the high frequency and small displacement oscillation fluid–structure interaction systems
Author(s) -
Shen Lin,
Wang Shu,
Feng Yuehong
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6936
Subject(s) - mathematics , displacement (psychology) , nonlinear system , oscillation (cell signaling) , mathematical analysis , compressibility , fluid–structure interaction , compact space , weak solution , mechanics , physics , finite element method , psychology , quantum mechanics , biology , psychotherapist , genetics , thermodynamics
The purpose of this paper is to study the fluid–structure interaction (FSI) problem which is a simplified model to describe high frequency and small displacement oscillation of elastic structure in fluids. The elastic structure displacement is modeled by a fourth‐order nonlinear hyperbolic square equations, the motion of fluid is modeled by the time‐dependent incompressible Navier–Stokes equations. We prove the existence of at least one weak solution (global in time) to this problem by compactness method. The result both holds for two‐dimensional and three‐dimensional cases.