ON AN EXISTENCE THEORY FOR A FLUID-BEAM PROBLEM ENCOMPASSING POSSIBLE CONTACTS

被引：11

作者：

Casanova, Jean-Jerome ^{[1
]}

Grandmont, Celine ^{[2
,3
]}

Hillairet, Matthieu ^{[4
]}

机构：

[1] PSL Res Univ, Univ Paris Dauphine, UMR CNRS 7534, CEREMADE, Pl Marechal de Lattre de Tassigny, F-75775 Paris 16, France

[2] Inria Paris, F-75012 Paris, France

[3] Sorbonne Univ, UMR 7598, LJLL, F-75005 Paris, France

[4] Univ Montpellier, IMAG, CNRS, Montpellier, France

来源：

JOURNAL DE L ECOLE POLYTECHNIQUE-MATHEMATIQUES | 2021年 / 8卷

关键词：

Incompressible Navier-Stokes equations; fluid-structure interactions; weak solutions; contact issue; WEAK SOLUTIONS; UNSTEADY INTERACTION; VISCOUS-FLUID;

D O I：

10.5802/jep.162

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we consider a coupled system of pdes modeling the interaction between a two-dimensional incompressible viscous fluid and a one-dimensional elastic beam located on the upper part of the fluid domain boundary. We design a functional framework to define weak solutions in case of contact between the elastic beam and the bottom of the fluid cavity. We then prove that such solutions exist globally in time regardless a possible contact by approximating the beam equation by a damped beam and letting this additional viscosity vanish.

引用

页码：933 / 971

页数：39

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