<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>This paper concerns the existence of global weak solutions <italic>á la Leray</italic> for compressible Navier–Stokes–Fourier systems with periodic boundary conditions and the truncated virial pressure law which is assumed to be thermodynamically unstable. More precisely, the main novelty is that the pressure law is not assumed to be monotone with respect to the density. This provides the first global weak solutions result for the compressible Navier-Stokes-Fourier system with such kind of pressure law which is strongly used as a generalization of the perfect gas law. The paper is based on a new construction of approximate solutions through an iterative scheme and fixed point procedure which could be very helpful to design efficient numerical schemes. Note that our method involves the recent paper by the authors published in Nonlinearity (2021) for the compactness of the density when the temperature is given.</p>
</abstract>

This paper concerns the existence of global weak solutions á la Leray for compressible Navier–Stokes–Fourier systems with periodic boundary conditions and the truncated virial pressure law which is assumed to be thermodynamically unstable. More precisely, the main novelty is that the pressure law is not assumed to be monotone with respect to the density. This provides the first global weak solutions result for the compressible Navier-Stokes-Fourier system with such kind of pressure law which is strongly used as a generalization of the perfect gas law. The paper is based on a new construction of approximate solutions through an iterative scheme and fixed point procedure which could be very helpful to design efficient numerical schemes. Note that our method involves the recent paper by the authors published in Nonlinearity (2021) for the compactness of the density when the temperature is given.

Global Existence of Weak Solutions for Compresssible Navier—Stokes—Fourier Equations with the Truncated Virial Pressure Law

Communications in Applied and Industrial Mathematics

This work is licensed under the Creative Commons Attribution 4.0 International License.

This paper concerns the existence of global weak solutions á la Leray for compressible Navier–Stokes–Fourier systems with periodic boundary conditions and the...

Global Existence of Weak Solutions for Compresssible Navier—Stokes—Fourier Equations with the Truncated Virial Pressure Law

Article Category: Research Article

Published Online: Jun 21, 2023

Page range: 17 - 49

Received: Nov 05, 2023

Accepted: Jan 06, 2023

DOI: https://doi.org/10.2478/caim-2023-0002

Keywords
Compressible Navier-Stokes, Heat-conduction, Truncated Virial pressure law, Non-monotone pressure, Vacuum state, Global weak solutions

© 2023 Didier Bresch et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Global Existence of Weak Solutions for Compresssible Navier—Stokes—Fourier Equations with the Truncated Virial Pressure Law

Article Category: Research Article

Published Online: Jun 21, 2023

Page range: 17 - 49

Received: Nov 05, 2023

Accepted: Jan 06, 2023

DOI: https://doi.org/10.2478/caim-2023-0002

KeywordsCompressible Navier-Stokes, Heat-conduction, Truncated Virial pressure law, Non-monotone pressure, Vacuum state, Global weak solutions

© 2023 Didier Bresch et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Keywords
Compressible Navier-Stokes, Heat-conduction, Truncated Virial pressure law, Non-monotone pressure, Vacuum state, Global weak solutions