Related papers: Anticipating stochastic equation of two-dimensiona…
The paper examines the issue of existence of solutions to the steady Navier-Stokes equations in an exterior domain in $\mathbb{R}^2$. The system is studied with nonhomogeneous slip boundary conditions. The main results proves the existence…
This article is devoted to the stochastic anticipating equations with the extended stochastic integral with respect to the Gaussian processes of a special type. In the particular cases the solutions of such an equations are the well-known…
In this article, we consider the stochastic wave equation on the real line driven by a linear multiplicative Gaussian noise, which is white in time and whose spatial correlation corresponds to that of a fractional Brownian motion with Hurst…
We introduce a family of stochastic models motivated by the study of nonequilibrium steady states of fluid equations. These models decompose the deterministic dynamics of interest into fundamental building blocks, i.e., minimal vector…
In this paper, we study the existence of solutions of stochastic incompressible non-Newtonian fluid models in $\mathbb{R}$. For the existence of solutions, we assume that the extra stress tensor $S$ is represented by $S({\mathbb A}) =…
The paper studies asymptotic properties of estimators of multidimensional stochastic differential equations driven by Brownian motions from high-frequency discrete data. Consistency and central limit properties of a class of estimators of…
A Lagrangian relativistic approach to the non--linear dynamics of cosmological perturbations of an irrotational collisionless fluid is considered. Solutions are given at second order in perturbation theory for the relevant fluid and…
Stochastic parametrisations of the interactions among disparate scales of motion in fluid convection are often used for estimating prediction uncertainty, which can arise due to inadequate model resolution, or incomplete observations,…
This paper investigates the nature of the development of two-dimensional steady flow of an incompressible fluid at the rear stagnation-point.
Strong existence and pathwise uniqueness of solutions with $L^{\infty}$-vorticity of 2D stochastic Euler equations is proved. The noise is multiplicative and involves first derivatives. A Lagrangian approach is implemented, where a…
This paper studies the second moment boundedness of solutions of linear stochastic delay differential equations. First, we give a framework, for general $\mathrm{N}$-dimensional linear stochastic differential equations with a single…
In this paper, we establish the existence and uniqueness of solutions to stochastic heat equations with logarithmic nonlinearity driven by Brownian motion on a bounded domain $D$ in the setting of $L^2(D)$ space. The result is valid for all…
We consider the Navier-Stokes system describing the motion of a compressible barotropic fluid driven by stochastic external forces. Our approach is semi-deterministic, based on solving the system for each fixed representative of the random…
It is shown that the incompressible Navier-Stokes equation can be derived from an infinite dimensional mean-field stochastic differential equation.
In this paper, a solution is given to reflected backward doubly stochastic differential equations when the barrier is not necessarily right-continuous, and the noise is driven by two independent Brownian motions and an independent Poisson…
The author studies the flows of an ideal incompressible fluid in a 2-dimensional domain, and in particular questions of instability and controllability.
In this paper, we are concerned with the local and global existence for the stochastic Prandtl equation in two and three dimensions, which governs the velocity field inside the boundary layer that appears in the inviscid limit of the…
A change of variables is introduced to reduce certain nonlinear stochastic evolution equations with multiplicative noise to the corresponding deterministic equation. The result is then used to investigate a stochastic porous medium…
This is an overview about natural sample spaces for differential equations driven by various noises. Appropriate sample spaces are needed in order to facilitate a random dynamical systems approach for stochastic differential equations. The…
These expository notes address certain stationary and ergodic properties of the equations of fluid dynamics subject to a spatially degenerate (i.e. frequency localized), white in time gaussian forcing. In order to provide an accessible…