On the weak solutions to the equations of a compressible heat conducting gas
Annales de l'I.H.P. Analyse non linéaire, Volume 32 (2015) no. 1, p. 225-243
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We consider the weak solutions to the Euler–Fourier system describing the motion of a compressible heat conducting gas. Employing the method of convex integration, we show that the problem admits infinitely many global-in-time weak solutions for any choice of smooth initial data. We also show that for any initial distribution of the density and temperature, there exists an initial velocity such that the associated initial-value problem possesses infinitely many solutions that conserve the total energy.

@article{AIHPC_2015__32_1_225_0,
     author = {Chiodaroli, Elisabetta and Feireisl, Eduard and Kreml, Ond\v rej},
     title = {On the weak solutions to the equations of a compressible heat conducting gas},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Elsevier},
     volume = {32},
     number = {1},
     year = {2015},
     pages = {225-243},
     doi = {10.1016/j.anihpc.2013.11.005},
     zbl = {1315.35160},
     mrnumber = {3303948},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_2015__32_1_225_0}
}
Chiodaroli, Elisabetta; Feireisl, Eduard; Kreml, Ondřej. On the weak solutions to the equations of a compressible heat conducting gas. Annales de l'I.H.P. Analyse non linéaire, Volume 32 (2015) no. 1, pp. 225-243. doi : 10.1016/j.anihpc.2013.11.005. http://www.numdam.org/item/AIHPC_2015__32_1_225_0/

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