Large Deviations and Higher Order Fluctuation Expansions for Conservative Stochastic PDEs

Real fluids contain small thermodynamic fluctuations on small scales. These fluctuations, governed by fluctuation-dissipation relations, introduce what is known as fluctuating hydrodynamics. This thesis is dedicated to investigating large deviations and higher order fluctuation expansions for conservative stochastic partial differential equations arising from fluctuating hydrodynamics. In particular, the thesis is divided into two parts. We studied large deviations for the Landau-Lifshitz-Navier-Stokes equations and higher-order fluctuation expansions for stochastic heat equations, respectively, in order to show the consistency of fluctuating hydrodynamic equations and interacting particle systems. Moreover, we provide relationships between probabilistic phenomena and the regularity features of deterministic or stochastic partial differential equations.

Level thesis:degree_level

thesis.doctoral

Grantor dc:publisher

Universität Bielefeld

Year

2024

Author dc:creator

• Wu, Zhengyan

Repository record source_url

https://pub.uni-bielefeld.de/record/2994677

OAI identifier oai:identifier

oai:pub.uni-bielefeld.de:2994677