  The main result of the present paper is a statement on existence, uniqueness
and regularity for mild solutions to a parabolic transport diffusion type
equation that involves a non-smooth coefficient. We investigate related Cauchy
problems on bounded smooth domains with Dirichlet boundary conditions by means
of semigroup theory and fixed point arguments. Main ingredients are the
definition of a product of a function and a (not too irregular) distribution as
well as a corresponding norm estimate. As an application, transport stochastic
partial differential equations driven by fractional Brownian noises are
considered in the pathwise sense.
