$L^{p}$-solutions of the Navier-Stokes equation with fractional Brownian noise

Abstract: We study the Navier-Stokes equations on a smooth bounded domain $D\subset \mathbb R<sup>d$ ($d=2$ or 3), under the effect of an additive fractional Brownian noise. We show local existence and uniqueness of a mild $L<sup>p$-solution for $p&gt;d$.