Magnetohydrodynamic turbulent flows: Existence results

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

“…Since then, stochastic partial differential equations and stochastic models of fluid dynamics have been the object of intense investigations which have generated several important results. We refer, for instance, to [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] . Similar investigations for Non-Newtonian fluids have almost not been undertaken except in very few work; we refer, for instance, to [23][24][25] for some computational studies of stochastic models of polymeric fluids.…”

On the Strong Solution for the 3D Stochastic Leray-Alpha Model

“…Here, the word "strong" means "strong" in the sense of the theory of stochastic differential equations, assuming that the stochastic processes are defined on a complete probability space and the Wiener process is given in advance. Since we consider the strong solution of the stochastic Leray-alpha equations, we do not need to use the techniques considered in the case of weak solutions see [5][6][7][8][9] . The techniques applied in this paper use in particular the properties of stopping times and some basic convergence principles from functional analysis see 10-13 .…”

Asymptotic behavior of solutions of stochastic evolution equations for second grade fluids

“…, .)) which is equivalent to the usual H 1 (D)-scalar product and the scalar product [11] or [13] for the definitions of these spaces. We denote by C any unessential positive constant independent of α, which may change from one line to the next.…”