TY - JOUR

T1 - Measure-valued solutions to the complete Euler system

AU - Březina, Jan

AU - Feireisl, Eduard

N1 - Funding Information:
2010 Mathematics Subject Classification. Primary 35L45; Secondary 35Q35, 76N15. Key Words and Phrases. Euler system, measure-valued solution, weak-strong uniqueness, perfect gas. 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.
Funding Information:
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.
Publisher Copyright:
© 2018 The Mathematical Society of Japan.

PY - 2018

Y1 - 2018

N2 - We introduce the concept of dissipative measure-valued so- lution 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.

AB - We introduce the concept of dissipative measure-valued so- lution 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.

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U2 - 10.2969/jmsj/77337733

DO - 10.2969/jmsj/77337733

M3 - Article

AN - SCOPUS:85055642951

VL - 70

SP - 1227

EP - 1245

JO - Journal of the Mathematical Society of Japan

JF - Journal of the Mathematical Society of Japan

SN - 0025-5645

IS - 4

ER -