Global Ill‐Posedness of the Isentropic System of Gas Dynamics
By Elisabetta Chiodaroli, Camillo De Lellis, Ondřej Kreml. 2013
248 citations recorded by the source corpus.
We consider the isentropic compressible Euler system in 2 space dimensions with pressure law p (ρ) = ρ2 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. © 2015 Wiley Periodicals, Inc.
Subfields: Applied Mathematics, Mathematical Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/4e7680f7c358e14d5391c259d6f05bc8af3a36ed
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In Applied Mathematics
- Martina Hofmanov'a
- Vlad Vicol
- T. Buckmaster
- Eduard Feireisl
- Dominic Breit
- Siddhartha Mishra
- Ulrik Skre Fjordholm
- Samuel Lanthaler
In Mathematical Physics
- Martina Hofmanov'a
- T. Buckmaster
- Vlad Vicol
- Samuel Lanthaler
- Siddhartha Mishra
- Eduard Feireisl
- Dominic Breit
- Maria Colombo
In Statistical and Nonlinear Physics
- Samuel Lanthaler
- Siddhartha Mishra
- Eduard Feireisl
- Martina Hofmanov'a
- Vlad Vicol
- T. Buckmaster
- Nikola B. Kovachki
Citations in the corpus
- Convex integration and phenomenologies in turbulence (2019, background): “The work [48], has since been extended and adapted by various authors to various problems arising in mathematical physics [46, 41, 181, 201, 27], see the reviews [47, 188, 50, 51] and references therein.”
- On solvability and ill-posedness of the compressible Euler system subject to stochastic forces (2017, background): “In particular, the barotropic Euler system in 2 and 3 space dimensions is ill-posed in the class of admissible entropy solutions (solutions dissipating energy) even for rather regular initial data, see Chiodaroli, De Lellis and Kreml [6], Chiodaroli and Kreml [7].”
- Statistical Solutions of Hyperbolic Conservation Laws: Foundations (2016, background): “Given the lack of global in time existence results, and the recent non-uniqueness results of [16, 17], the acceptance of entropy solutions as the standard solution paradigm for multi-dimensional systems of conservation laws is being increasingly questioned.”