A note on measure-valued solutions to the full Euler system

Václav Mácha; Emil Wiedemann

Applications of Mathematics (2022)

  • Volume: 67, Issue: 4, page 419-430
  • ISSN: 0862-7940

Abstract

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We construct two particular solutions of the full Euler system which emanate from the same initial data. Our aim is to show that the convex combination of these two solutions form a measure-valued solution which may not be approximated by a sequence of weak solutions. As a result, the weak* closure of the set of all weak solutions, considered as parametrized measures, is not equal to the space of all measure-valued solutions. This is in stark contrast with the incompressible Euler equations.

How to cite

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Mácha, Václav, and Wiedemann, Emil. "A note on measure-valued solutions to the full Euler system." Applications of Mathematics 67.4 (2022): 419-430. <http://eudml.org/doc/298320>.

@article{Mácha2022,
abstract = {We construct two particular solutions of the full Euler system which emanate from the same initial data. Our aim is to show that the convex combination of these two solutions form a measure-valued solution which may not be approximated by a sequence of weak solutions. As a result, the weak* closure of the set of all weak solutions, considered as parametrized measures, is not equal to the space of all measure-valued solutions. This is in stark contrast with the incompressible Euler equations.},
author = {Mácha, Václav, Wiedemann, Emil},
journal = {Applications of Mathematics},
keywords = {measure-valued solution; compressible Euler system},
language = {eng},
number = {4},
pages = {419-430},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A note on measure-valued solutions to the full Euler system},
url = {http://eudml.org/doc/298320},
volume = {67},
year = {2022},
}

TY - JOUR
AU - Mácha, Václav
AU - Wiedemann, Emil
TI - A note on measure-valued solutions to the full Euler system
JO - Applications of Mathematics
PY - 2022
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 67
IS - 4
SP - 419
EP - 430
AB - We construct two particular solutions of the full Euler system which emanate from the same initial data. Our aim is to show that the convex combination of these two solutions form a measure-valued solution which may not be approximated by a sequence of weak solutions. As a result, the weak* closure of the set of all weak solutions, considered as parametrized measures, is not equal to the space of all measure-valued solutions. This is in stark contrast with the incompressible Euler equations.
LA - eng
KW - measure-valued solution; compressible Euler system
UR - http://eudml.org/doc/298320
ER -

References

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