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

• Published in: Communications in partial differential equations Vol. 47; no. 8; pp. 1591 - 1635
• Main Authors: Mácha, Václav, Muha, Boris, Nečasová, Šárka, Roy, Arnab, Trifunović, Srđan
• Format: Journal Article
• Language: English
• Published: Philadelphia Taylor & Francis 04.08.2022; Taylor & Francis Ltd
• Subjects: Compressible fluids; Conducting fluids; Decoupling; Domains; Fluid-structure interaction; Heat exchange; Heat transmission; heat-conducting fluid; Navier-Stokes-Fourier system; Thermoelasticity; Time dependence
• ISSN: 0360-5302; 1532-4133
• DOI: 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.