Geodesic
Stability of planar rarefaction waves under general viscosity perturbation of the isentropic Euler system
Feireisl, Eduard1, 2 ; Novotný, Antonín3
1 a Institute of Mathematics of the Academy of Sciences of the Czech Republic, Žitná 25, CZ-115 67 Praha 1, Czech Republic
2 b Institute of Mathematics, Technische Universität Berlin, Straße des 17. Juni 136, 10623 Berlin, Germany
3 c Université de Toulon, IMATH, EA 2134, BP 20132, 83957 La Garde, France
Annales de l'I.H.P. Analyse non linéaire, novembre – décembre 2021, Tome 38 (2021) no. 6, pp. 1725-1737

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We consider the vanishing viscosity limit for a model of a general non-Newtonian compressible fluid in Rd, d=2,3. We suppose that the initial data approach a profile determined by the Riemann data generating a planar rarefaction wave for the isentropic Euler system. Under these circumstances the associated sequence of dissipative solutions approaches the corresponding rarefaction wave strongly in the energy norm in the vanishing viscosity limit. The result covers the particular case of a linearly viscous fluid governed by the Navier–Stokes system.

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DOI : 10.1016/j.anihpc.2021.01.001
Keywords: Vanishing viscosity limit, Non–linear viscous fluid, Rarefaction wave, Isentropic Euler system

Feireisl, Eduard 1, 2 ; Novotný, Antonín 3

1 a Institute of Mathematics of the Academy of Sciences of the Czech Republic, Žitná 25, CZ-115 67 Praha 1, Czech Republic
2 b Institute of Mathematics, Technische Universität Berlin, Straße des 17. Juni 136, 10623 Berlin, Germany
3 c Université de Toulon, IMATH, EA 2134, BP 20132, 83957 La Garde, France 
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     author = {Feireisl, Eduard and Novotn\'y, Anton{\'\i}n},
     title = {Stability of planar rarefaction waves under general viscosity perturbation of the isentropic {Euler} system},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {1725--1737},
     publisher = {Elsevier},
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Feireisl, Eduard; Novotný, Antonín. Stability of planar rarefaction waves under general viscosity perturbation of the isentropic Euler system. Annales de l'I.H.P. Analyse non linéaire, novembre – décembre 2021, Tome 38 (2021) no. 6, pp. 1725-1737. doi: 10.1016/j.anihpc.2021.01.001

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