The existence of a weak solution for a compressible multicomponent fluid structure interaction problem

0584372 - MÚ 2025 RIV NL eng J - Journal Article
Kalousek, Martin - Mitra, Sourav - Nečasová, Šárka
The existence of a weak solution for a compressible multicomponent fluid structure interaction problem.
Journal de Mathematiques Pures et Appliquees. Roč. 184, April (2024), s. 118-189. ISSN 0021-7824. E-ISSN 1776-3371
R&D Projects: GA ČR(CZ) GA22-01591S
Grant - others:AV ČR(CZ) AP2101
Program: Akademická prémie - Praemium Academiae
Institutional support: RVO:67985840
Keywords : fluid-structure interaction * two-fluid model * global weak solutions
OECD category: Pure mathematics
Impact factor: 2.3, year: 2022
Method of publishing: Limited access
https://doi.org/10.1016/j.matpur.2024.02.007

We analyze 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 a system resembling compressible Navier-Stokes equations with a physically realistic pressure depending on densities of both the fluids. The shell possesses a non-linear, non-convex Koiter energy. Considering that the densities are comparable initially we prove the existence of a weak solution until the degeneracy of the energy or the self-intersection of the structure occurs for two cases. In the first case the adiabatic exponents are assumed to satisfy max⁡{γ,β}>2, min⁡{γ,β}>0, and the structure involved is assumed to be non-dissipative. For the second case we assume the critical case max⁡{γ,β}≥2 and min⁡{γ,β}>0 and the dissipativity of the structure. The result is achieved in several steps involving, extension of the physical domain, penalization of the interface condition, artificial regularization of the shell energy and the pressure, the almost compactness argument, added structural dissipation and suitable limit passages depending on uniform estimates.
Permanent Link: https://hdl.handle.net/11104/0352289