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

0558262 - MÚ 2023 RIV CZ eng J - Journal Article
Mácha, Václav - Wiedemann, E.
A note on measure-valued solutions to the full Euler system.
Applications of Mathematics. Roč. 67, č. 4 (2022), s. 419-430. ISSN 0862-7940. E-ISSN 1572-9109
R&D Projects: GA ČR(CZ) GA18-05974S
Institutional support: RVO:67985840
Keywords : measure-valued solution * compressible Euler system
OECD category: Pure mathematics
Impact factor: 0.7, year: 2022
Method of publishing: Limited access
https://dx.doi.org/10.21136/AM.2021.0279-20

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.
Permanent Link: http://hdl.handle.net/11104/0331995