Existence of a weak solution to a nonlinear fluid-structure interaction problem with heat exchange. Issue 8 (4th August 2022)

• Record Type: Journal Article
• Authors: Mácha, Václav; Muha, Boris; Nečasová, Šárka; Roy, Arnab; Trifunović, Srđan
• Is Part Of: Communications in partial differential equations. Volume 47:Issue 8(2022)
• Page Start: 1591
• Page End: 1635
• Publication Date: 2022-08-04
• Subjects: fluid-structure interaction -- heat-conducting fluid -- Navier-Stokes-Fourier system -- thermoelasticity; Differential equations, Partial -- Periodicals; 515.353
• DOI: 10.1080/03605302.2022.2068425
• Languages: English
• ISSNs: 0360-5302

Abstract

Abstract: 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.