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
SN - 0025-5645
VL - 70
SP - 1227
EP - 1245
JO - Journal of the Mathematical Society of Japan
JF - Journal of the Mathematical Society of Japan
IS - 4
ER -