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 xed point arguments. Main ingredients are the denition 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.
Cite this article
Elena Issoglio, Transport Equations with Fractal Noise - Existence, Uniqueness and Regularity of the Solution. Z. Anal. Anwend. 32 (2013), no. 1, pp. 37–53DOI 10.4171/ZAA/1473