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Weak–strong uniqueness for the isentropic Euler equations with possible vacuum

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Abstract

We establish a weak–strong uniqueness result for the isentropic compressible Euler equations, that is: As long as a sufficiently regular solution exists, all energy-admissible weak solutions with the same initial data coincide with it. The main novelty in this contribution, compared to previous literature, is that we allow for possible vacuum in the strong solution.

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Data sharing not applicable to this article as no datasets were generated or analysed during the current study.

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Acknowledgements

SSG and AJ acknowledge the support of the Department of Atomic Energy, Government of India, under project no. 12-R &D-TFR-5.01-0520. SSG would like to thank Inspire faculty-research grant DST/INSPIRE/04/2016/000237. We would like to thank anonymous referees for their comments and suggestions.

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Authors and Affiliations

  1. Centre for Applicable Mathematics, Tata Institute of Fundamental Research, Sharadanagar, Post Bag No 6503, Bangalore, 560065, India

    Shyam Sundar Ghoshal & Animesh Jana

  2. Institute of Applied Analysis, Ulm University, Helmholtzstr. 18, 89081, Ulm, Germany

    Emil Wiedemann

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  1. Shyam Sundar Ghoshal
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  2. Animesh Jana
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  3. Emil Wiedemann
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Correspondence to Shyam Sundar Ghoshal.

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This article is part of the section “Theory of PDEs” edited by Eduardo Teixeira.

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Ghoshal, S.S., Jana, A. & Wiedemann, E. Weak–strong uniqueness for the isentropic Euler equations with possible vacuum. Partial Differ. Equ. Appl. 3, 54 (2022). https://doi.org/10.1007/s42985-022-00191-2

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  • DOI: https://doi.org/10.1007/s42985-022-00191-2

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