no. 5
Analysis of the adiabatic piston problem via methods of continuum mechanics
Annales de l'I.H.P. Analyse non linéaire, Tome 35 (2018) no. 5, pp. 1377-1408.

We consider a system modelling the motion of a piston in a cylinder filled by a viscous heat conducting gas. The piston is moving longitudinally without friction under the influence of the forces exerted by the gas. In addition, the piston is supposed to be thermally insulating (adiabatic piston). This fact raises several challenges which received a considerable attention, essentially in the statistical physics literature. We study the problem via the methods of continuum mechanics, specifically, the motion of the gas is described by means of the Navier–Stokes–Fourier system in one space dimension, coupled with Newton's second law governing the motion of the piston. We establish global in time existence of strong solutions and show that the system stabilizes to an equilibrium state for t→∞.

DOI : 10.1016/j.anihpc.2017.11.008
Mots clés : Piston problem, Navier–Stokes–Fourier system, Free boundary problem 
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     title = {Analysis of the adiabatic piston problem via methods of continuum mechanics},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {1377--1408},
     publisher = {Elsevier},
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Feireisl, Eduard; Mácha, Václav; Nečasová, Šárka; Tucsnak, Marius. Analysis of the adiabatic piston problem via methods of continuum mechanics. Annales de l'I.H.P. Analyse non linéaire, Tome 35 (2018) no. 5, pp. 1377-1408. doi : 10.1016/j.anihpc.2017.11.008. http://archive.numdam.org/articles/10.1016/j.anihpc.2017.11.008/

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