On Non-uniqueness of Continuous Entropy Solutions to the Isentropic Compressible Euler Equations View Full Text


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Article Info

DATE

2022-07-02

AUTHORS

Vikram Giri, Hyunju Kwon

ABSTRACT

We consider the Cauchy problem for the isentropic compressible Euler equations in a three-dimensional periodic domain under general pressure laws. For any smooth initial density away from the vacuum, we construct infinitely many entropy solutions with no presence of shock. In particular, the constructed density is smooth and the momentum is α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}-Hölder continuous for α<1/7\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha <1/7$$\end{document}. Also, we provide a continuous entropy solution satisfying the entropy inequality strictly. More... »

PAGES

1213-1283

References to SciGraph publications

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  • 2022-04-22. Nonuniqueness and Existence of Continuous, Globally Dissipative Euler Flows in ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
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    http://scigraph.springernature.com/pub.10.1007/s00205-022-01802-3

    DOI

    http://dx.doi.org/10.1007/s00205-022-01802-3

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