# $\mathbb{L}^p$-solutions for stochastic Navier-Stokes equations with jump noise

## TL;DR

This paper establishes the existence and uniqueness of solutions to 2D stochastic Navier-Stokes equations driven by jump noise using an $ ext{L}^p$-framework, allowing for weaker assumptions on noise and initial data.

## Contribution

It introduces an $ ext{L}^p$-approach to solve stochastic Navier-Stokes equations with jump noise, improving upon traditional methods by relaxing assumptions.

## Key findings

- Proves existence and uniqueness of solutions in an $ ext{L}^p$-setting.
- Handles irregular jump noise with weaker initial data assumptions.
- Provides a new framework for stochastic fluid dynamics with jump noise.

## Abstract

We study the existence and uniqueness of solutions of 2D Stochastic Navier-Stokes equation with space irregular jump noise for initial data in certain Sobolev spaces of negative order. Comparing with the Galerkin approximation method, the main advantage of this work is to use an $\mathbb{L}^p$-setting to obtain the solution under much weaker assumptions on the noise and the initial condition.