In this paper we prove the stochastic homeomorphism flow property and the strong Feller
property for stochastic differential equations with sigular time dependent drifts and Sobolev …

A theory of Ruelle–Pollicott (RP) resonances for stochastic differential systems is presented.
These resonances are defined as the eigenvalues of the generator (Kolmogorov operator) of …

The multiscale variability of the ocean circulation due to its nonlinear dynamics remains a
big challenge for theoretical understanding and practical ocean modeling. This paper …

Consider the stochastic evolution equation in a separable Hilbert space H with a nice
multiplicative noise and a locally Dini continuous drift. We prove that for any initial data the …

We consider the stochastic divergence-free continuity equations with Ladyzhenskaya–Prodi–
Serrin condition. Wellposedness is proved meanwhile uniqueness may fail for the …

This paper is concerned with stochastic differential equations (SDEs for short) with irregular
coefficients. By utilising a functional analytic approximation approach, we establish the …

In this paper we prove global bounds on the spatial gradient of viscosity solutions to second
order linear and nonlinear parabolic equations in (0, T)× R N. Our assumptions include the …

The results established by Flandoli, Gubinelli and Priola (2010)[17] for stochastic transport
equation with bounded and Hölder continuous drift are generalized to bounded and Dini …

We deal with the 3D inviscid Leray-α model. The well posedness for this problem is not
known; by adding a random perturbation we prove that there exists a unique (in law) global …

The spectrum of the generator (Kolmogorov operator) of a diffusion process, referred to as
the Ruelle-Pollicott (RP) spectrum, provides a detailed characterization of correlation …