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…