Nonuniqueness of admissible weak solution to the Riemann problem for the full Euler system in two dimensions

0524230 - MÚ 2021 RIV US eng J - Článek v odborném periodiku
Al Baba, Hind - Klingenberg, C. - Kreml, Ondřej - Mácha, Václav - Markfelder, S.
Nonuniqueness of admissible weak solution to the Riemann problem for the full Euler system in two dimensions.
SIAM Journal on Mathematical Analysis. Roč. 52, č. 2 (2020), s. 1729-1760. ISSN 0036-1410. E-ISSN 1095-7154
Grant CEP: GA ČR(CZ) GJ17-01694Y
GRANT EU: European Commission(XE) 320078 - MATHEF
Institucionální podpora: RVO:67985840
Klíčová slova: compressible Euler system * nonuniqueness * Riemann problem
Obor OECD: Pure mathematics
Impakt faktor: 1.860, rok: 2020
Způsob publikování: Omezený přístup
https://doi.org/10.1137/18M1190872

The question of well- and ill-posedness of entropy admissible solutions to the multi-dimensional systems of conservation laws has been studied recently in the case of isentropic Euler equations. In this context special initial data were considered, namely the 1D Riemann problem which is extended trivially to a second space dimension. It was shown that there exist infinitely many bounded entropy admissible weak solutions to such a 2D Riemann problem for isentropic Euler equations if the initial data give rise to a 1D self-similar solution containing a shock. In this work we study such a 2D Riemann problem for the full Euler system in two space dimensions and prove the existence of infinitely many bounded entropy admissible weak solutions in the case that the Riemann initial data give rise to the 1D self-similar solution consisting of two shocks and possibly a contact discontinuity.
Trvalý link: http://hdl.handle.net/11104/0308617