Abstract
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 γ>12/7 (γ>1 in two dimensions). The solution exists until the moving boundary approaches a self-intersection.
This provides a compressible counterpart of the results in [D. Lengeler, M. Ruzicka, Weak Solutions for an Incompressible Newtonian Fluid Interacting with a Koiter Type Shell. Arch. Ration. Mech. Anal. 211 (2014), no. 1, 205--255] on incompressible Navier--Stokes equations.
Original language | English |
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Pages (from-to) | 1-68 |
Number of pages | 68 |
Journal | Archive for Rational Mechanics and Analysis |
Early online date | 29 Nov 2017 |
DOIs | |
Publication status | E-pub ahead of print - 29 Nov 2017 |