The stochastic convective Brinkman-Forchheimer (SCBF) equations or the tamed Navier-
Stokes equations in bounded or periodic domains are considered in this work. We show the …

We introduce a new framework of Markovian lifts of stochastic Volterra integral equations
(SVIEs for short) with completely monotone kernels. We define the state space of the …

This paper focuses on a class of stochastic functional differential equations with infinite
delay and non-Lipschitz coefficients. Under one-sided super-linear growth and non …

The asymptotic log-Harnack inequality is established for several kinds of models on
stochastic differential systems with infinite memory: non-degenerate SDEs, neutral SDEs …

By using the asymptotic coupling method, the asymptotic log-Harnack inequality is
established for the transition semigroup associated to the 3D Leray-α model with fractional …

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 …

Due to technical reasons, existing results concerning Harnack type inequalities for SPDEs
with multiplicative noise apply only to the case where the coefficient in the noise term is a …

The asymptotic log-Harnack inequality is established for SPDE with degenerate
multiplicative noise by the coupling method. As applications, the gradient estimate …

The asymptotic log-Harnack inequality is proved for Leray-α model with degenerate type
noise using the asymptotic coupling method. In particular, we don't impose any lower bound …

Consider d-dimensional magneto-hydrodynamic (MHD) equations with fractional
dissipations driven by multiplicative noise. First, we prove the existence of martingale …