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Global III-posedness of the isentropic system of gas dynamics


Chiodaroli, Elisabetta; De Lellis, Camillo; Kreml, Ondřej (2015). Global III-posedness of the isentropic system of gas dynamics. Communications on Pure and Applied Mathematics, 68(7):1157-1190.

Abstract

We consider the isentropic compressible Euler system in 2 space dimensions with pressure law p ($\rho$) = $\rho$$^2$ and we show the existence of classical Riemann data, i.e. pure jump discontinuities across a line, for which there are infinitely many admissible bounded weak solutions (bounded away from the void). We also show that some of these Riemann data are generated by a 1-dimensional compression wave: our theorem leads therefore to Lipschitz initial data for which there are infinitely many global bounded admissible weak solutions.

Abstract

We consider the isentropic compressible Euler system in 2 space dimensions with pressure law p ($\rho$) = $\rho$$^2$ and we show the existence of classical Riemann data, i.e. pure jump discontinuities across a line, for which there are infinitely many admissible bounded weak solutions (bounded away from the void). We also show that some of these Riemann data are generated by a 1-dimensional compression wave: our theorem leads therefore to Lipschitz initial data for which there are infinitely many global bounded admissible weak solutions.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:15 May 2015
Deposited On:27 Jan 2016 11:15
Last Modified:14 Feb 2018 10:09
Publisher:Wiley-Blackwell Publishing, Inc.
ISSN:0010-3640
OA Status:Green
Publisher DOI:https://doi.org/10.1002/cpa.21537

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