Existence of a weak solution to a nonlinear fluid-structure interaction problem with heat exchange

0559954 - MÚ 2023 RIV US eng J - Journal Article
Mácha, Václav - Muha, B. - Nečasová, Šárka - Roy, Arnab - Trifunovic, S.
Existence of a weak solution to a nonlinear fluid-structure interaction problem with heat exchange.
Communications in Partial Differential Equations. Roč. 47, č. 8 (2022), s. 1591-1635. ISSN 0360-5302. E-ISSN 1532-4133
R&D Projects: GA ČR(CZ) GA19-04243S
Grant - others:AV ČR(CZ) AP2101
Program: Akademická prémie - Praemium Academiae
Institutional support: RVO:67985840
Keywords : fluid-structure interaction * heat-conducting fluid * Navier-Stokes-Fourier system * thermoelasticity
OECD category: Pure mathematics
Impact factor: 1.9, year: 2022
Method of publishing: Open access
https://doi.org/10.1080/03605302.2022.2068425

In this paper, we study a nonlinear interaction problem between a thermoelastic shell and a heat-conducting fluid. The shell is governed by linear thermoelasticity equations and encompasses a time-dependent domain which is filled with a fluid governed by the full Navier-Stokes-Fourier system. The fluid and the shell are fully coupled, giving rise to a novel nonlinear moving boundary fluid-structure interaction problem involving heat exchange. The existence of a weak solution is obtained by combining three approximation techniques–decoupling, penalization and domain extension. In particular, the penalization and the domain extension allow us to use the methods already developed for compressible fluids on moving domains. In such a way, the proof is more elegant and the analysis is drastically simplified. Let us stress that this is the first time the heat exchange in the context of fluid-structure interaction problems is considered.
Permanent Link: https://hdl.handle.net/11104/0333077