<em>L_p</em>-solutions of the Navier-Stokes equation with fractional Brownian noise

Abstract

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

Keywords

• stochastic partial di erential equations| Navier-Stokes equations| mild solution| fractional Brownian motion