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<p>We consider the three-dimensional fluid–structure interaction system modeling a system consisting of a viscous incompressible fluid and an elastic plate forming its moving upper boundary. The fluid is described by the incompressible Navier–Stokes equations with a free upper boundary that evolves according to the motion of the structure, coupled via the velocity- and stress-matching conditions. We show that under a rather general condition on the initial data, there exists a global-in-time weak solution of the system. In particular, there is no contact between the plate and the bottom boundary.</p>

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A Global Existence Result on Weak Solutions for the 3D Navier–Stokes-Plate System with no Contact

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月26日

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  • Mario Bukal,
  • Igor Kukavica,
  • Linfeng Li,
  • Boris Muha

摘要

We consider the three-dimensional fluid–structure interaction system modeling a system consisting of a viscous incompressible fluid and an elastic plate forming its moving upper boundary. The fluid is described by the incompressible Navier–Stokes equations with a free upper boundary that evolves according to the motion of the structure, coupled via the velocity- and stress-matching conditions. We show that under a rather general condition on the initial data, there exists a global-in-time weak solution of the system. In particular, there is no contact between the plate and the bottom boundary.