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Non-uniqueness of admissible weak solutions to the compressible Euler equations with smooth initial data Kreml, Ondřej
Description
We consider the isentropic Euler equations of gas dynamics in the whole two-dimensional space and we prove the existence of a $C^\infty$ initial datum which admits infinitely many bounded admissible weak solutions. Taking advantage of the relation between smooth solutions to the Euler system and to the Burgers equation we construct a smooth compression wave which collapses into a perturbed Riemann state at some time instant $T > 0$. In order to continue the solution after the formation of the discontinuity, we adjust and apply the theory developed by De Lellis and Székelyhidi and we construct infinitely many solutions. </p>
This is a joint work with Elisabetta Chiodaroli, V\'aclav M\'acha and Sebastian Schwarzacher. </p>
Item Metadata
Title |
Non-uniqueness of admissible weak solutions to the compressible Euler equations with smooth initial data
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2020-11-23T10:27
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Description |
We consider the isentropic Euler equations of gas dynamics in the whole two-dimensional space and we prove the existence of a $C^\infty$ initial datum which admits infinitely many bounded admissible weak solutions. Taking advantage of the relation between smooth solutions to the Euler system and to the Burgers equation we construct a smooth compression wave which collapses into a perturbed Riemann state at some time instant $T > 0$. In order to continue the solution after the formation of the discontinuity, we adjust and apply the theory developed by De Lellis and Székelyhidi and we construct infinitely many solutions. </p> This is a joint work with Elisabetta Chiodaroli, V\'aclav M\'acha and Sebastian Schwarzacher. </p> |
Extent |
22.0 minutes
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Subject | |
Type | |
File Format |
video/mp4
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Language |
eng
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Notes |
Author affiliation: Czech Academy of Sciences
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Series | |
Date Available |
2021-05-23
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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DOI |
10.14288/1.0398132
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URI | |
Affiliation | |
Peer Review Status |
Unreviewed
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Scholarly Level |
Other
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Rights URI | |
Aggregated Source Repository |
DSpace
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Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International