Cooper Faile

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math.AP2026

The unique limit of the Glimm-Lax construction for Sobolev data and obstructions to 1-d convex integration

Jeffrey Cheng, Cooper Faile, Sam G. Krupa

We consider a genuinely nonlinear $1$ -d system of hyperbolic conservation laws with two unknowns. A famous construction of Glimm & Lax shows that global-in-time "Glimm-Lax" weak en…

math.AP2025

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

Geng Chen, Cooper Faile, Sam G. Krupa

For hyperbolic systems of conservation laws, including important physical models from continuum mechanics, the question of stability for large data solutions remains a challenging…

math.AP2025

Solutions to conservation laws are HÃ¶lder-stable in $L^{2}$ in the weak-BV setting

Geng Chen, Cooper Faile, Sam G. Krupa

We consider hyperbolic systems of conservation laws in one spatial dimension. For any limit of front tracking solutions $v$ , and for a general weak solution $u \in L^{\infty}$ with no…

The unique limit of the Glimm-Lax construction for Sobolev data and obstructions to 1-d convex integration

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

Solutions to conservation laws are HÃ¶lder-stable in L2 in the weak-BV setting

Solutions to conservation laws are HÃ¶lder-stable in $L^{2}$ in the weak-BV setting