# Well-posedness by noise for scalar conservation laws

## TL;DR

This paper demonstrates that adding noise to scalar conservation laws with irregular flux functions ensures well-posedness, addressing issues of non-uniqueness in deterministic cases.

## Contribution

It establishes that stochastic perturbations can restore well-posedness for scalar conservation laws with low regularity flux functions.

## Key findings

- Noise induces well-posedness in otherwise ill-posed scalar conservation laws.
- Perturbation by noise leads to uniqueness of entropy solutions.
- The approach applies to systems with spatially inhomogeneous flux functions.

## Abstract

We consider stochastic scalar conservation laws with spatially inhomogeneous flux. The regularity of the flux function with respect to its spatial variable is assumed to be low, so that entropy solutions are not necessarily unique in the corresponding deterministic scalar conservation law. We prove that perturbing the system by noise leads to well-posedness.