Open Access
October, 2018 Measure-valued solutions to the complete Euler system
J. Math. Soc. Japan 70(4): 1227-1245 (October, 2018). DOI: 10.2969/jmsj/77337733


We introduce the concept of dissipative measure-valued solution to the complete Euler system describing the motion of an inviscid compressible fluid. These solutions are characterized by a parameterized (Young) measure and a dissipation defect in the total energy balance. The dissipation defect dominates the concentration errors in the equations satisfied by the Young measure. A dissipative measure-valued solution can be seen as the most general concept of solution to the Euler system retaining its structural stability. In particular, we show that a dissipative measure-valued solution necessarily coincides with a classical one on its life span provided they share the same initial data.

Funding Statement

The second author leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013)/ ERC Grant Agreement 320078. The Institute of Mathematics of the Academy of Sciences of the Czech Republic is supported by RVO:67985840.


Download Citation

Jan BŘEZINA. Eduard FEIREISL. "Measure-valued solutions to the complete Euler system." J. Math. Soc. Japan 70 (4) 1227 - 1245, October, 2018.


Received: 15 February 2017; Published: October, 2018
First available in Project Euclid: 13 July 2018

zbMATH: 1408.35134
MathSciNet: MR3868717
Digital Object Identifier: 10.2969/jmsj/77337733

Primary: 35L45
Secondary: 35Q35 , 76N15

Keywords: Euler system , measure-valued solution , perfect gas , weak-strong uniqueness

Rights: Copyright © 2018 Mathematical Society of Japan

Vol.70 • No. 4 • October, 2018
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