Existence of a weak solution for a compressible multicomponent fluid-structure interaction problem

Abstract: I will speak about our recent work on the analysis 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 modeled by compressible Navier-Stokes equations with a physically realistic pressure depending on the densities of both fluids. The shell constitutes the boundary of the fluid domain, and it possesses a non-linear, non-convex Koiter energy (of a quite general form). We are interested in the existence of a weak solution to the system until the time-dependent boundary approaches a self-intersection. We first prove a global existence result (until a degeneracy occurs) when the adiabatic exponents solve max{γ, β} > 2 and min{γ, β} > 0, and further, the densities are comparable. Next, with a slightly extra regularity assumption on the initial structural displacement, we extend our global existence result to the case max{γ, β} ≥ 2 and min{γ, β} > 0. In the first part of the talk, I will try to introduce the classical theory on the existence of weak solutions for compressible mono-fluid models. Next, I will talk about our work on the multi-component FSI problem. This is joint work with M. Kalousek and Š. Nečasová.

MathematicsPhysics

Audience: researchers in the topic

Nečas Seminar on Continuum Mechanics

Series comments: This seminar was founded on December 14, 1966.

Faculty of Mathematics and Physics, Charles University, Sokolovská 83, Prague 8. If not written otherwise, we will meet on Mondays at 15:40 in lecture hall K3 (2nd floor).