Compressible Fluids Interacting with a Linear-Elastic Shell

被引:38
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
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
收藏
页码:495 / 562
页数:68
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