Random dynamics of two-dimensional stochastic second grade fluids

Weak Solutions of a Stochastic Model for Two-Dimensional Second Grade Fluids

Strong solution for a stochastic model of two-dimensional second grade fluids : existence, uniqueness and asymptotic behaviour

We investigate a stochastic evolution equation for the motion of a second grade fluid filling a bounded domain of R. Global existence and uniqueness of strong probabilistic solution is established. In contrast to previous results on this model we show that the sequence of Galerkin approximation converges in mean square to the exact strong probabilistic solution of the problem. We also give two ...

Problem of Second Grade Fluids in Convex Polyhedrons

This article studies the solutions of a three-dimensional grade-two fluid model with a tangential boundary condition, in a polyhedron. We begin to split the problem into a system with a generalized Stokes problem and a transport equation, as V. Girault and L.R. Scott in the two dimensions case. But, compared to the two-dimensional problem, we have an additional term difficult to bound, which re...

Localization dynamics of fluids in random confinement.

The dynamics of two-dimensional fluids confined within a random matrix of obstacles is investigated using both colloidal model experiments and molecular dynamics simulations. By varying fluid and matrix area fractions in the experiment, we find delocalized tracer particle dynamics at small matrix area fractions and localized motion of the tracers at high matrix area fractions. In the delocalize...

Numerical solution of second-order stochastic differential equations with Gaussian random parameters

In this paper, we present the numerical solution of ordinary differential equations (or SDEs), from each order especially second-order with time-varying and Gaussian random coefficients. We indicate a complete analysis for second-order equations in special case of scalar linear second-order equations (damped harmonic oscillators with additive or multiplicative noises). Making stochastic differe...