  We prove existence and uniqueness results for (mild) solutions to some
non-linear parabolic evolution equations with a rough forcing term. Our method
of proof relies on a careful exploitation of the interplay between the spatial
and time regularity of the solution by capitialising some of Kato's ideas in
semigroup theory. Classical Young integration theory is then shown to provide a
means of interpreting the equation. As an application we consider the three
dimensional Navier-Stokes system with a stochastic forcing term arising from a
fractional Brownian motion with h > 1/2.
