# On the small time asymptotics of scalar stochastic conservation laws

## TL;DR

This paper establishes small time large deviation principles for scalar stochastic conservation laws with multiplicative noise, using the doubling of variables method to analyze their asymptotic behavior.

## Contribution

It introduces a novel application of the doubling of variables method to derive small time large deviation principles for these laws.

## Key findings

- Proves small time large deviation principles for scalar stochastic conservation laws.
- Demonstrates the effectiveness of the doubling of variables method in this context.
- Provides a framework for analyzing asymptotic behaviors of stochastic PDEs.

## Abstract

In this paper, we establish a small time large deviation principles for scalar stochastic conservation laws driven by multiplicative noise. The doubling of variables method plays a key role.