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In this paper, we prove a sharp and strong non-uniqueness for a class of weak solutions to the incompressible Navier-Stokes equations in $\R^3$. To be more precise, we exhibit the non-uniqueness result in a strong sense, that is, any weak…
We consider a discrete time dynamic system described by a difference equation with periodic coefficients and with additive stochastic noise. We investigate the possibility of the periodicity for the solution. In particular, we found…
This paper investigates the long-time dynamics of solutions for an abstract nonlinear stochastic hydrodynamic-type equation driven by multiplicative L\'{e}vy noise. The framework encompasses several key hydrodynamical models, including the…
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We establish the existence and uniqueness for a one-dimensional stochastic differential equation driven by a Brownian motion and a pure jump {\levy} process. It is shown that under fairly general conditions on the coefficients, pathwise…
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Properties of an infinite system of nonlinearly coupled ordinary differential equations are discussed. This system models some properties present in the equations of motion for an inviscid fluid such as the skew symmetry and the…
This paper is a continuation of [26]. Here theorems on conditional uniqueness and regularity for solutions to stochastic Navier-Stokes equations in $\mathbb R^d$ are presented.
We present a simple uniqueness argument for a collection of McKean-Vlasov problems that have seen recent interest. Our first result shows that, in the weak feedback regime, there is global uniqueness for a very general class of random…
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We consider randomly forced 2D Navier-Stokes equations in a bounded domain with smooth boundary. It is assumed that the random perturba- tion is non-degenerate, and its law is periodic in time and has a support localised with respect to…
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