On the Motion of Compressible Fluid in a Moving Domain and Applications to Fluid-Structure Interaction

Problems of fluid flow inside a moving domain deserve a lot of interest as they appear in many practical applications. Such problems can also be seen as a preparation step for research of fluid-structure interaction problems. Research of the compressible version of the Navier-Stokes system dates back to the nineties when the groundbreaking result of the existence of the global weak solutions to the compressible barotropic Navier--Stokes system on a fixed domain was proved by P. L.Lions and, later, by E. Feireisl and collaborators who extended the existence result to more physically relevant state equations.

After that the theory of weak solutions was extended to the problem of fluid flow inside a moving domain. Such existing theory was applied to more complicated problems e.g. to the interaction between a system of heat-conducting fluid with a shell of Koiter type, or into the case of one or two compressible mutually noninteracting fluids and a shell of Koiter type encompassing a time-dependent 3D domain filled by the fluids.

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