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

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.