Existence of global solutions for some hyperbolic systems via novel regularizations

We discuss the global existence of weak (entropy) solutions for two distinct classes of hyper-bolic systems by constructing novel viscous regularizations.In the first part of the talk, we focus on a class of 2 × 2 Keyfitz-Kranzer systems arising in thinfilm flows. Because the standard diagonal viscous approximation fails to yield the appropriatemathematical structure, we instead construct a novel viscous regularization inspired by lubrica-tion equations. This approach provides the critical compactness estimates necessary to establishthe existence of weak entropy solutions via the vanishing diffusion limit [1].In the second part of the talk, we generalize these results to n×n systems of a broader Keyfitz-Kranzer class covering several important physical models. We introduce a new artificial viscousregularization aligned with the nonlinear field, which yields a parabolic equation for the Riemanninvariant associated with the nonlinear field, coupled with transport equations for the remainingRiemann invariants. This structure drives the compactness argument and yields global existenceof weak solutions for the inviscid system [2].References[1] R. Barthwal, P. ¨Offner, and C. Rohde. Global existence for a class of Keyfitz–Kranzersystems. Accepted for publication at Journal of Hyperbolic Differential Equations, 2026.[2] R. Barthwal and L. Sahu. Well-posedness for a class of n × n hyperbolic systems and shockstability for the viscous approximation. arXiv preprint arXiv:2609.13989, 2026