Kremp, H. K. (2023, September 19). A nonlinear SPDE approximation of the Dean-Kawasaki equation [Presentation]. Second Berlin-Leipzig Workshop on Fluctuating Hydrodynamics, Freie Universität Berlin, Germany. http://hdl.handle.net/20.500.12708/188715
Second Berlin-Leipzig Workshop on Fluctuating Hydrodynamics
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Event date:
19-Sep-2023 - 20-Sep-2023
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Event place:
Freie Universität Berlin, Germany
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Keywords:
Dean-Kawasaki equation; weak error estimates
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Abstract:
In this talk we consider a nonlinear SPDE approximation of the Dean-Kawasaki equation for independent particles. Our approximation satisfies the physical constraints of the particle system, i.e. its solution is a probability measure for all times (preservation of positivity and mass conservation). Using a duality argument, we prove that the weak error between particle system and nonlinear SPDE is of the order N{-1-1/(d/2+1)} log(N). Along the way we show well-posedness, a comparison principle and an entropy estimate for a class of nonlinear regularized Dean-Kawasaki equations with Itô noise.
This is joint work together with Ana Djurdjevac and Nicolas Perkowski.
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Project title:
Regularisierung durch Rauschen: Diskrete und stetige Systeme: P34992-N (FWF Fonds zur Förderung der wissenschaftlichen Forschung (FWF))
