Zeitschrift für Analysis und ihre Anwendungen
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Published online: 2013-01-27
Transport Equations with Fractal Noise - Existence, Uniqueness and Regularity of the SolutionElena Issoglio (1) King's College London, UK
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.
Keywords: Transport equation, non-smooth coefficients, fractional Brownian noise, stochastic partial differential equation
Issoglio Elena: Transport Equations with Fractal Noise - Existence, Uniqueness and Regularity of the Solution. Z. Anal. Anwend. 32 (2013), 37-53. doi: 10.4171/ZAA/1473