Large Deviation Principle For Stochastic Models Of Second Grade Fluids

The second grade fluids is an admissible model of slow flow fluids,which contains industrial fluids,slurries,polymer melts,etc..The second grade fluid has general and pleasant properties such as boundedness,stability and exponential decay,and also has interesting connections with other fluid models.The theory of large deviations is an important branch of probability theory,which concerns the asymptotic behaviour of remote tails of sequences of probability distri-butions.It has important applications in many areas,such as in thermodynamics,sta-tistical mechanics,information theory and risk management,etc..In 1970s,Freidlin and Wentzell derived both the sample path diffusion large deviation principle and the asymptotics of problem of exit from a domain.After that,the theory of small perturba-tion large deviations for stochastic(partial)differential equations has been extensively developed.Like the large deviations,the moderate deviations are very useful in the theory of statistics.The moderate deviations approximation bridge the gap between a central limit approximation and a large deviations approximation.It provides us with the rate of convergence and a useful method for constructing asymptotic confidence intervals.In this thesis,we studied the large deviation principle for stochastic models of 2-D second grade fluids,including the central limit theory and the moderate deviation principle of 2-D second grade fluids driven by Brownian Motion,the large deviation principle and the moderate deviation principle for 2-D second grade fluids driven by Lévy noise.