Transport equations with fractal noise-existence, uniqueness and regularity of the solution
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Publication:1940974
DOI10.4171/ZAA/1473zbMATH Open1260.35261arXiv1107.3788WikidataQ59901987 ScholiaQ59901987MaRDI QIDQ1940974
Author name not available (Why is that?)
Publication date: 11 March 2013
Published in: (Search for Journal in Brave)
Abstract: 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.
Full work available at URL: https://arxiv.org/abs/1107.3788
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