Special Session 27: Recent Trends in Navier-Stokes Equations, Euler Equations, and Related Problems

Existence of weak solutions for a compressible multi-component fluid structure interaction problem

Martin Kalousek
Institute of Mathematics, Czech Academy of Sciences
Czech Rep
Co-Author(s):    Sourav Mitra, \v S\` arka Ne\v casov\`a
Abstract:
We address the question of global in time existence of weak solutions of a system of PDEs governing the interaction between two compressible mutually noninteracting fluids and a shell of Koiter type encompassing a time dependent 3D domain filled by the fluids. The dynamics of the fluids is modelled by compressible Navier-Stokes equations with a physically realistic pressure depending on densities of both the fluids. The shell constitutes the boundary of the fluid domain and it possesses a non-linear, non-convex Koiter energy.