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arXiv · 2509.16432

Quantitative weak-BV stability of "wild'' solutions to compressible Euler equations, with a view towards higher systems

Geng Chen·Cooper Faile·Sam G. Krupa
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Abstract

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 H\"older 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 with additional conserved quantities.

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Geng Chen, Cooper Faile, Sam G. Krupa. 2025-09-19. Quantitative weak-BV stability of "wild'' solutions to compressible Euler equations, with a view towards higher systems. https://arxiv.org/abs/2509.16432

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