# Kinetic solutions for nonlocal stochastic conservation laws

## TL;DR

This paper investigates the existence and uniqueness of kinetic solutions for scalar conservation laws with nonlocal super-critical diffusion and multiplicative noise, using double variables analysis and parabolic approximation methods.

## Contribution

It introduces a novel approach to establish existence and uniqueness of solutions for nonlocal stochastic conservation laws with super-critical diffusion.

## Key findings

- Proved uniqueness of kinetic solutions using double variables method.
- Established existence through parabolic approximation.
- Extended the theory to include nonlocal super-critical diffusion with noise.

## Abstract

This work is devoted to examine the uniqueness and existence of kinetic solutions for a class of scalar conservation laws involving a nonlocal super-critical diffusion operator and a multiplicative noise. Our proof for uniqueness is based upon the analysis on double variables method and the existence is enabled by a parabolic approximation.