[Stabilité quantitative BV-faible des solutions non régulières de grande amplitude aux équations d’Euler compressibles, dans la perspective de systèmes supérieurs]
For hyperbolic systems of conservation laws, including important physical models from continuum mechanics, the question of stability for large data solutions remains a challenging open problem. In recent work [arXiv:2507.23645] the authors introduce a framework for showing Hölder stability of potentially “wild” large data solutions, relative to a class of BV solutions, for systems with two conserved quantities. This is referred to as “weak-BV” stability. In this paper, we give a short introduction to the methods while applying them to the “full” Euler system with three conserved quantities. We discuss applications to future work for higher systems (i.e. systems with more than two conserved quantities).
Pour les systèmes hyperboliques de lois de conservation, y compris les modèles physiques importants issus de la mécanique des milieux continus, la question de la stabilité des solutions de grande amplitude reste un problème ouvert difficile à résoudre. Dans des travaux récents [arXiv:2507.23645], les auteurs présentent un cadre permettant de démontrer la stabilité de type Hölder pour des solutions de classe BV, sujettes à des perturbations non régulières de grande amplitude, pour des systèmes à deux quantités conservées. Cette propriété s’appelle stabilité « BV faible ». Dans cet article, nous présentons brièvement ces méthodes tout en les appliquant au système « complet » d’Euler avec trois quantités conservées. Nous discutons des applications à des travaux futurs pour des systèmes d’ordre plus élevés (c’est-à-dire des systèmes comportant plus de deux quantités conservées).
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Keywords: Stability, systems of conservation law, full Euler system
Mots-clés : Stabilité, systèmes hyperboliques de lois de conservation, système complet d’Euler
Geng Chen 1 ; Cooper Faile 2 ; Sam G. Krupa 3
CC-BY 4.0
Geng Chen; Cooper Faile; Sam G. Krupa. Quantitative weak-BV stability of “wild” solutions to compressible Euler equations, with a view towards higher systems. Comptes Rendus. Mathématique, Volume 364 (2026), pp. 673-687. doi: 10.5802/crmath.854
@article{CRMATH_2026__364_G3_673_0,
author = {Geng Chen and Cooper Faile and Sam G. Krupa},
title = {Quantitative {weak-BV} stability of {\textquotedblleft}wild{\textquotedblright} solutions to compressible {Euler} equations, with a view towards higher systems},
journal = {Comptes Rendus. Math\'ematique},
pages = {673--687},
year = {2026},
publisher = {Acad\'emie des sciences, Paris},
volume = {364},
doi = {10.5802/crmath.854},
language = {en},
}
TY - JOUR AU - Geng Chen AU - Cooper Faile AU - Sam G. Krupa TI - Quantitative weak-BV stability of “wild” solutions to compressible Euler equations, with a view towards higher systems JO - Comptes Rendus. Mathématique PY - 2026 SP - 673 EP - 687 VL - 364 PB - Académie des sciences, Paris DO - 10.5802/crmath.854 LA - en ID - CRMATH_2026__364_G3_673_0 ER -
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