Thermal effects in fluid structure interactions
Analysis of PDEs
2026-02-12 v2
Abstract
In this article we consider two different heat conducting fluids each modelled by the incompressible Navier-Stokes-Fourier system separated by a non-linear elastic Koiter shell. The motion of the shell changes the domain of definition of the two separated fluids. For this setting we show the existence of a weak solution. The heat capacity of the shell is given energetically. It allows to consider transmission laws ranging from insulation to superconductivity.We follow a variational approach for fluid-structure interactions. To include temperature a novel two step minimization scheme is used to produce an approximation. The weak solutions are energetically closed and include a strictly positive temperature.
Cite
@article{arxiv.2510.04801,
title = {Thermal effects in fluid structure interactions},
author = {Sourav Mitra and Sebastian Schwarzacher},
journal= {arXiv preprint arXiv:2510.04801},
year = {2026}
}