2025/10/28 by Fjordholm, Ulrik S., Ørke, Magnus C.
#35L65 #60H15 #60H50 #Analysis of PDEs (math.AP) #FOS: Mathematics
paper · doi:10.48550/arxiv.2510.24475
Scalar conservation laws sit at the intersection between being simple enough to study analytically, while being complex enough to exhibit a wide range of nonlinear phenomena. We introduce a novel stochastic perturbation of scalar conservation laws, inspired by mean field games. We prove well-posedness of the stochastically perturbed equation; prove that it converges as the noise parameter is sent to 0; and that the limit is the unique entropy solution of the conservation law. Thus, the noise acts as a selection criterion for (deterministic) conservation laws. This is the first such result for nonlinear hyperbolic conservation laws.