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Existence of global weak solutions for the high frequency and small displacement oscillation fluid-structure interactions systems
  • Lin Shen,
  • Shu Wang,
  • Yuehong Feng
Lin Shen
Beijing University of Technology
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Shu Wang
Beijing University of Technology
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Yuehong Feng
Beijing University of Technology
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Peer review status:UNDER REVIEW

10 Mar 2020Submitted to Mathematical Methods in the Applied Sciences
13 Mar 2020Assigned to Editor
13 Mar 2020Submission Checks Completed
27 Mar 2020Reviewer(s) Assigned
03 Jul 2020Review(s) Completed, Editorial Evaluation Pending

Abstract

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 solutions (global in time) to this problem by compactness method. The result both holds for two-dimensional and three-dimensional cases.