Non-uniqueness of energy-conservative solutions to the isentropic compressible two-dimensional Euler equations
2018 ◽
Vol 15
(04)
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pp. 721-730
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Keyword(s):
We consider the 2-d isentropic compressible Euler equations. It was shown in [E. Chiodaroli, C. De Lellis and O. Kreml, Global ill-posedness of the isentropic system of gas dynamics, Comm. Pure Appl. Math. 68(7) (2015) 1157–1190] that there exist Riemann initial data as well as Lipschitz initial data for which there exist infinitely many weak solutions that fulfill an energy inequality. In this paper, we will prove that there is Riemann initial data for which there exist infinitely many weak solutions that conserve energy, i.e. they fulfill an energy equality. As in the aforementioned paper, we will also show that there even exist Lipschitz initial data with the same property.
2021 ◽
Vol 18
(03)
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pp. 701-728
Keyword(s):
2011 ◽
Vol 08
(04)
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pp. 671-690
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2009 ◽
Vol 29
(4)
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pp. 777-802
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1999 ◽
pp. 757-766
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2004 ◽
Vol 175
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pp. 125-164
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Numerical Solution of Compressible Euler Equations by High Order Nodal Discontinuous Galerkin Method
2013 ◽
Vol 392
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pp. 165-169
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1993 ◽
Vol 59
(566)
◽
pp. 2990-2996
1994 ◽
Vol 60
(571)
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pp. 872-878