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The main result of the present paper is a statement on existence, uniquenessand regularity for mild solutions to a parabolic transport diffusion typeequation that involves a non-smooth coefficient. We investigate related Cauchyproblems on bounded smooth domains with Dirichlet boundary conditions by meansof semigroup theory and fixed point arguments. Main ingredients are thedefinition of a product of a function and a (not too irregular) distribution aswell as a corresponding norm estimate. As an application, transport stochasticpartial differential equations driven by fractional Brownian noises areconsidered in the pathwise sense.

Transport equations with fractal noise - existence, uniqueness and regularity of the solution