On the Existence of Strong Solutions to a Fluid Structure Interaction Problem with Navier Boundary Conditions

被引：7

作者：

Djebour, Imene Aicha ^{[1
]}

Takahashi, Takeo ^{[1
]}

机构：

[1] Univ Lorraine, CNRS, INRIA, IECL, F-54000 Nancy, France

来源：

JOURNAL OF MATHEMATICAL FLUID MECHANICS | 2019年 / 21卷 / 03期

关键词：

Navier-Stokes system; Damped beam equation; Strong solutions; FINITE-ELEMENT APPROXIMATION; STOKES EQUATIONS; WEAK SOLUTIONS; SOLID SYSTEMS; STABILIZATION; REGULARITY; COLLISION; BODIES; FLOW;

D O I：

10.1007/s00021-019-0440-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a fluid-structure interaction system composed by a three-dimensional viscous incompressible fluid and an elastic plate located on the upper part of the fluid boundary. The fluid motion is governed by the Navier-Stokes system whereas we add a damping in the plate equation. We use here Navier-slip boundary conditions instead of the standard no-slip boundary conditions. The main results are the local in time existence and uniqueness of strong solutions of the corresponding system and the global in time existence and uniqueness of strong solutions for small data and if we assume the presence of frictions in the boundary conditions.

引用

页数：30

共 50 条

[1] On the Existence of Strong Solutions to a Fluid Structure Interaction Problem with Navier Boundary Conditions
Imene Aicha Djebour
Takéo Takahashi
[J]. Journal of Mathematical Fluid Mechanics, 2019, 21
[2] EXISTENCE OF STRONG SOLUTIONS FOR A COMPRESSIBLE FLUID-SOLID INTERACTION SYSTEM WITH NAVIER SLIP BOUNDARY CONDITIONS
Djebour, Imene Aicha
[J]. EVOLUTION EQUATIONS AND CONTROL THEORY, 2024, 13 (04): : 1162 - 1198
[3] Existence of a weak solution to a fluid-elastic structure interaction problem with the Navier slip boundary condition
Muha, Boris
Canic, Suncica
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2016, 260 (12) : 8550 - 8589
[4] Local Existence of Strong Solutions of a Fluid–Structure Interaction Model
Sourav Mitra
[J]. Journal of Mathematical Fluid Mechanics, 2020, 22
[5] On the Existence of Strong Solutions to a Coupled Fluid-Structure Evolution Problem
da Veiga, H. Beirao
[J]. JOURNAL OF MATHEMATICAL FLUID MECHANICS, 2004, 6 (01) : 21 - 52
[6] On the Existence of Strong Solutions to a Coupled Fluid-Structure Evolution Problem
H. Beirão da Veiga
[J]. Journal of Mathematical Fluid Mechanics, 2004, 6 : 21 - 52
[7] Local strong solutions to the stochastic third grade fluid equations with Navier boundary conditions
Tahraoui, Yassine
Cipriano, Fernanda
[J]. STOCHASTICS AND PARTIAL DIFFERENTIAL EQUATIONS-ANALYSIS AND COMPUTATIONS, 2024, 12 (03): : 1699 - 1744
[8] Local Existence of Strong Solutions of a Fluid-Structure Interaction Model
Mitra, Sourav
[J]. JOURNAL OF MATHEMATICAL FLUID MECHANICS, 2020, 22 (04)
[9] Existence and uniqueness of solutions to the damped Navier–Stokes equations with Navier boundary conditions for three dimensional incompressible fluid
Subha Pal
Rajib Haloi
[J]. Journal of Applied Mathematics and Computing, 2021, 66 : 307 - 325
[10] SOLUTIONS TO A FLUID-STRUCTURE INTERACTION FREE BOUNDARY PROBLEM
Kukavica, Igor
Tuffaha, Amjad
[J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2012, 32 (04) : 1355 - 1389

← 1 2 3 4 5 →