# Regularization by noise in (2x 2) hyperbolic systems of conservation law

## TL;DR

This paper demonstrates that stochastic perturbation can regularize non-strict hyperbolic systems of conservation laws, establishing existence and uniqueness of solutions without requiring initial BV-regularity, marking a first in the field.

## Contribution

It introduces the concept of regularization by noise in hyperbolic conservation laws and proves existence and uniqueness without initial BV-regularity assumptions.

## Key findings

- Existence and uniqueness of solutions established
- Regularization effect of noise demonstrated
- First result on noise-induced regularization in hyperbolic systems

## Abstract

In this paper we study a non strictly systems of conservation law by stochastic perturbation. We show the existence and uniqueness of the solution. We do not assume that $BV$-regularity for the initial conditions. The proofs are based on the concept of entropy solution and in the characteristics method (in the influence of noise). This is the first result on the regularization by noise in hyperbolic systems of conservation law.