Large deviations for stochastic 3D Leray-<inline-formula><tex-math id="M1">\begin{document}$ \alpha $\end{document}</tex-math></inline-formula> model with fractional dissipation

Abstract

In this paper we establish the Freidlin-Wentzell's large deviation principle for stochastic 3D Leray-α model with general fractional dissipation and small multiplicative noise. This model is the stochastic 3D Navier-Stokes equations regularized through a smoothing kernel of order θ 1 in the nonlinear term and a θ 2-fractional Laplacian. The main result generalizes the corresponding LDP result of the classical stochastic 3D Leray-α model (θ 1 = 1, θ 2 = 1), and it is also applicable to the stochastic 3D hyperviscous Navier-Stokes equations (θ 1 = 0, θ 2 ≥ 5 4) and stochastic 3D critical Leray-α model (θ 1 = 1 4 , θ 2 = 1).

Small time asymptotics for SPDEs with locally monotone coefficients

“…Due to its wide applications in extremal events arising in risk management, mathematical finance, statistical mechanics, quantum physics and many other areas, large deviation theory has become an important component of modern applied probability, see, e.g. [5,6,11,14,21,22,23,25,36,52,55,57] and references therein.…”