Existence of a weak solution to a nonlinear fluid-structure interaction problem with heat exchange. (English) Zbl 1504.35358
Summary: 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.
MSC:
| 35Q35 | PDEs in connection with fluid mechanics |
| 35Q74 | PDEs in connection with mechanics of deformable solids |
| 76A10 | Viscoelastic fluids |
| 76N10 | Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics |
| 74F10 | Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) |
| 74K25 | Shells |
| 74B20 | Nonlinear elasticity |
| 74A15 | Thermodynamics in solid mechanics |
| 35D30 | Weak solutions to PDEs |
Keywords:
fluid-structure interaction; heat-conducting fluid; Navier-Stokes-Fourier system; thermoelasticityReferences:
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