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<p>We consider the Cauchy problem for an inviscid irrotational fluid on a domain with a free boundary governed by a fourth order linear elasticity equation. We first derive the Craig-Sulem-Zakharov formulation of the problem and then establish the existence of a global weak solution in two space dimensions for the fluid, in the general case without a damping term, for any initial data with finite energy.</p>

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Global-in-Time Weak Solutions for an Inviscid Free Surface Fluid-Structure Problem Without Damping

  • 期刊论文

  • 发表日期：

    2025年5月13日

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  • Thomas Alazard,
  • Igor Kukavica,
  • Amjad Tuffaha

摘要

We consider the Cauchy problem for an inviscid irrotational fluid on a domain with a free boundary governed by a fourth order linear elasticity equation. We first derive the Craig-Sulem-Zakharov formulation of the problem and then establish the existence of a global weak solution in two space dimensions for the fluid, in the general case without a damping term, for any initial data with finite energy.