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

Thomas Alazard; Igor Kukavica; Amjad Tuffaha

doi:10.1007/s40818-025-00207-1

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

Thomas Alazard
, Igor Kukavica
, Amjad Tuffaha

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Article number	15
Journal	Annals of PDE
Volume	11
Issue number	1
DOIs	https://doi.org/10.1007/s40818-025-00207-1
Publication status	Published - 1 Jun 2025
Externally published	Yes

Keywords

Dirichlet to Neumann operator
Free boundary problem
Weak solutions

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10.1007/s40818-025-00207-1

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

abstract = "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.",

keywords = "Dirichlet to Neumann operator, Free boundary problem, Weak solutions",

author = "Thomas Alazard and Igor Kukavica and Amjad Tuffaha",

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AU - Kukavica, Igor

AU - Tuffaha, Amjad

N1 - Publisher Copyright: © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2025.

PY - 2025/6/1

Y1 - 2025/6/1

N2 - 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.

AB - 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.

KW - Dirichlet to Neumann operator

KW - Free boundary problem

KW - Weak solutions

UR - https://www.scopus.com/pages/publications/105004899257

U2 - 10.1007/s40818-025-00207-1

DO - 10.1007/s40818-025-00207-1

M3 - Article

AN - SCOPUS:105004899257

SN - 2524-5317

VL - 11

JO - Annals of PDE

JF - Annals of PDE

IS - 1

M1 - 15

ER -

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

Abstract

Keywords

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