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- Publisher
- Springer Journals
- Copyright
- Copyright © The Author(s), under exclusive licence to Springer Nature B.V. part of Springer Nature 2021
- ISSN
- 0167-8019
- eISSN
- 1572-9036
- DOI
- 10.1007/s10440-021-00394-6
- Publisher site
- See Article on Publisher Site
Abstract
We study the evolutionary compressible Navier–Stokes–Fourier system in a bounded two-dimensional domain with the pressure law p(ϱ,θ)∼ϱθ+ϱlogα(1+ϱ)+θ4\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$p(\varrho ,\theta ) \sim \varrho \theta + \varrho \log ^{\alpha }(1+ \varrho )+ \theta ^{4}$\end{document}. We consider the weak solutions with entropy inequality and total energy balance. We show the existence of this type of weak solutions without any restriction on the size of the initial conditions or the right-hand sides provided α>17+41716≅2.34\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$\alpha > \frac{17+\sqrt{417}}{16}\cong 2.34$\end{document}.
Journal
Acta Applicandae Mathematicae – Springer Journals
Published: Feb 17, 2021