We establish verifiable general sufficient conditions for exponential or subexponential
ergodicity of Markov processes that may lack the strong Feller property. We apply the …

We study the long time statistics of a class of semi–linear damped wave equations with
polynomial nonlinearities and perturbed by additive Gaussian noise in dimensions 2 and 3 …

We study a class of semi-linear differential Volterra equations with polynomial-type
potentials that incorporates the effects of memory while being subjected to random …

We establish the dual notions of scaling and saturation from geometric control theory in an
infinite-dimensional setting. This generalization is applied to the low-mode control problem …

We construct an invariant measure μ for the Surface Quasi-Geostrophic (SQG) equation and
show that almost all functions in the support of μ are initial conditions of global, unique …

We consider the three-dimensional magnetohydrodynamics (MHD) equations in the
presence of a spatially degenerate stochastic forcing as a model for magnetostrophic …

In this paper, an asymptotic log-Harnack inequality and some consequent properties are
established via the asymptotic coupling method for a class of stochastic 2D hydrodynamical …

We investigate the stability of statistically stationary conductive states for Rayleigh–Bénard
convection that arise due to a bulk stochastic internal heating. Our results indicate that …

Some recent developments in the analysis of long-time behaviors of stochastic solutions of
nonlinear conservation laws driven by stochastic forcing are surveyed. The existence and …

We consider the long time statistics of a one-dimensional stochastic Ginzburg-Landau
equation with cubic nonlinearity while being subjected to random perturbations via an …