Dissipative measure-valued solutions for general conservation laws
Gwiazda, Piotr1 ; Kreml, Ondřej2 ; Świerczewska-Gwiazda, Agnieszka3
1 Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-656 Warszawa, Poland
2 Institute of Mathematics of the Academy of Sciences of the Czech Republic, Žitná 25, CZ-115 67 Praha 1, Czech Republic
3 Institute of Applied Mathematics and Mechanics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland
Annales de l'I.H.P. Analyse non linéaire, Tome 37 (2020) no. 3, pp. 683-707.
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In the last years measure-valued solutions started to be considered as a relevant notion of solutions if they satisfy the so-called measure-valued – strong uniqueness principle. This means that they coincide with a strong solution emanating from the same initial data if this strong solution exists. This property has been examined for many systems of mathematical physics, including incompressible and compressible Euler system, compressible Navier-Stokes system et al. and there are also some results concerning general hyperbolic systems. Our goal is to provide a unified framework for general systems, that would cover the most interesting cases of systems, and most importantly, we give examples of equations, for which the aspect of measure-valued – strong uniqueness has not been considered before, like incompressible magnetohydrodynamics and shallow water magnetohydrodynamics.

DOI : 10.1016/j.anihpc.2019.11.001
Mots-clés : Young measures, Measure-valued solutions, Hyperbolic systems
Gwiazda, Piotr 1 ; Kreml, Ondřej 2 ; Świerczewska-Gwiazda, Agnieszka 3

1 Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-656 Warszawa, Poland
2 Institute of Mathematics of the Academy of Sciences of the Czech Republic, Žitná 25, CZ-115 67 Praha 1, Czech Republic
3 Institute of Applied Mathematics and Mechanics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland 
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Gwiazda, Piotr; Kreml, Ondřej; Świerczewska-Gwiazda, Agnieszka. Dissipative measure-valued solutions for general conservation laws. Annales de l'I.H.P. Analyse non linéaire, Tome 37 (2020) no. 3, pp. 683-707. doi : 10.1016/j.anihpc.2019.11.001. http://archive.numdam.org/articles/10.1016/j.anihpc.2019.11.001/

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