Applications of Mathematics, Vol. 67, No. 4, pp. 419-430, 2022
A note on measure-valued solutions to the full Euler system
Václav Mácha, Emil Wiedemann
Received September 29, 2020. Published online September 6, 2021.
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.
Keywords: measure-valued solution; compressible Euler system
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Affiliations: Václav Mácha (corresponding author), Institute of Mathematics of the Czech Academy of Sciences, Žitná 25, 115 67 Praha 1, Czech Republic, e-mail: macha@math.cas.cz; Emil Wiedemann, Ulm University, Institute of Applied Analysis, Helmholtzstr. 18, 89081 Ulm, Germany, e-mail: emil.wiedemann@uni-ulm.de
