Compressible fluid-structure interactions

• Applicants: Professor Dr. Dominic Breit; Dr. Prince Romeo Mensah
• Subject Area: Mathematics
• Term: since 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 543675748

We consider the interaction of a viscous compressible fluid with a flexible shell in three space dimensions. The fluid is described by the isentropic Navier-Stokes equations in a domain that is changing in accordance with the motion of the structure. The displacement of the latter evolves along a visco-elastic shell equation. Both are coupled through kinematic boundary conditions and the balance of forces. We allow for a general geometric set-up, where the structure can even occupy the complete boundary. In the first step, we plan to prove the well-posedness of the underlying system. First, we will prove the existence of local-in-time strong solutions in smooth function spaces. Eventually, we turn to the weak-strong uniqueness property: We aim to prove that a weak and a strong solution emanating from the same data coincide provided both exist. The existence of weak solutions satisfying an energy inequality is known from a previous work of the first-named applicant. Finally, we will analyze the conditional regularity of weak solutions with the aim of finding regularity assumptions under which there is no blow-up in finite time. In a final work package, we shall extend these results to the case of heat-conducting fluids, where the fluid phase is described by the full Navier-Stokes-Fourier system. In this case, the absolute temperature appears as an additional unknown and the internal energy/entropy balance is added to the set of equations.

• DFG Programme: Research Grants