ﻻ يوجد ملخص باللغة العربية
We establish the existence and uniqueness of local strong pathwise solutions to the stochastic Boussinesq equations with partial diffusion term forced by multiplicative noise on the torus in $mathbb{R}^{d},d=2,3$. The solution is strong in both PDE and probabilistic sense.In the two dimensional case, we prove the global existence of strong solutions to the Boussinesq equations forced by additive noise using a suitable stochastic analogue of a logarithmic Gronwalls lemma. After the global existence and uniqueness of strong solutions are established, the large deviation principle (LDP) is proved by the weak convergence method. The weak convergence is shown by a tightness argument in the appropriate functional space.
Averaging is an important method to extract effective macroscopic dynamics from complex systems with slow modes and fast modes. This article derives an averaged equation for a class of stochastic partial differential equations without any Lipschitz a
This paper is devoted to investigating the Freidlin-Wentzells large deviation principle for a class of McKean-Vlasov quasilinear SPDEs perturbed by small multiplicative noise. We adopt the variational framework and the modified weak convergence crite
This paper is devoted to proving the strong averaging principle for slow-fast stochastic partial differential equations with locally monotone coefficients, where the slow component is a stochastic partial differential equations with locally monotone
In this paper, we investigate the convergence of the global large solution to its associated constant equilibrium state with an explicit decay rate for the compressible Navier-Stokes equations in three-dimensional whole space. Suppose the initial dat
In this paper we consider an alternative formulation of a class of stochastic wave and master equations with scalar noise that are used in quantum optics for modelling open systems and continuously monitored systems. The reformulation is obtained by