Compressible Fluids Interacting with a Linear-Elastic Shell

被引：41

作者：

Breit, Dominic ^{[1
]}

Schwarzacher, Sebastian ^{[2
]}

机构：

[1] Heriot Watt Univ, Dept Math, Edinburgh EH14 4AS, Midlothian, Scotland

[2] Charles Univ Prague, Fac Math & Phys, Dept Anal, Sokolovska 83, Prague 18675, Czech Republic

来源：

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS | 2018年 / 228卷 / 02期

关键词：

NAVIER-STOKES EQUATIONS; KOITER TYPE SHELL; WEAK SOLUTIONS; VISCOUS-FLUID; UNSTEADY INTERACTION; EXISTENCE; DOMAINS; SYSTEM; ENERGY; MOTION;

D O I：

10.1007/s00205-017-1199-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the Navier-Stokes equations governing the motion of an isentropic compressible fluid in three dimensions interacting with a flexible shell of Koiter type. The latter one constitutes a moving part of the boundary of the physical domain. Its deformation is modeled by a linearized version of Koiter's elastic energy. We show the existence of weak solutions to the corresponding system of PDEs provided the adiabatic exponent satisfies gamma > 12/7 (gamma > 1 in two dimensions). The solution exists until the moving boundary approaches a self-intersection. This provides a compressible counterpart of the results in Lengeler and Ruzicka (Arch Ration Mech Anal 211(1):205-255, 2014) on incompressible Navier-Stokes equations.

引用

页码：495 / 562

页数：68

共 50 条

[41] TIME-PERIODIC WEAK SOLUTIONS FOR AN INCOMPRESSIBLE NEWTONIAN FLUID INTERACTING WITH AN ELASTIC PLATE\ast [J].

Mindrila, Claudiu ;

Schwarzacher, Sebastian .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2022, 54 (04) :4139-4162

[42] WEAK-STRONG UNIQUENESS FOR AN ELASTIC PLATE INTERACTING WITH THE NAVIER-STOKES EQUATION\ast [J].

Schwarzacher, Sebastian ;

Sroczinski, Matthias .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2022, 54 (04) :4104-4138

[43] A note on complete bounded trajectories and attractors for compressible self-gravitating fluids [J].

Guo, Rongcong ;

Jiang, Fei ;

Yin, Junping .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2012, 75 (04) :1933-1944

[44] Global classical solutions to the compressible micropolar viscous fluids with large oscillations and vacuum [J].

Zhu, Canze ;

Tao, Qiang .

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2023, 46 (01) :28-53

[45] Multiple Scales and Singular Limits for Compressible Rotating Fluids with General Initial Data [J].

Feireisl, Eduard ;

Novotny, Antonin .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2014, 39 (06) :1104-1127

[46] Effect of Prestresses on Generalized Lamb Waves in an Elastic Compressible Layer Interacting with a Viscous Liquid Layer [J].

Bagno, O. M. .

INTERNATIONAL APPLIED MECHANICS, 2023, 59 (04) :417-428

[47] LONGITUDINAL-RADIAL VIBRATIONS OF THE ELASTIC CYLINDRICAL SHELL FILLED WITH A VISCOUS COMPRESSIBLE FLUID [J].

Khudoynazarov, Kh Kh ;

Khalmuradov, R., I ;

Yalgashev, B. F. .

VESTNIK TOMSKOGO GOSUDARSTVENNOGO UNIVERSITETA-MATEMATIKA I MEKHANIKA-TOMSK STATE UNIVERSITY JOURNAL OF MATHEMATICS AND MECHANICS, 2021, (69) :139-154

[48] The finite weak solutions for the compressible micropolar fluids model [J].

Su, Jingrui ;

Yang, Yanjiong .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2025, 548 (01)

[49] The Cauchy problem for the nonisentropic compressible MHD fluids: Optimal time-decay rates [J].

Huang, Wenting ;

Fu, Shengbin .

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2023, 46 (08) :9708-9735

[50] Large-time behaviour of solutions to a class of non-Newtonian compressible fluids [J].

Guo, Shanshan ;

Tan, Zhong .

NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2017, 24 (03)

← 1 2 3 4 5 →