Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 932053, 27 pages
Research Article

On Stochastic Models Describing the Motions of Randomly Forced Linear Viscoelastic Fluids

Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria 0002, South Africa

Received 19 August 2009; Accepted 16 March 2010

Academic Editor: Jewgeni Dshalalow

Copyright © 2010 P. A. Razafimandimby. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper is devoted to the analysis of stochastic equations describing the motions of a large class of incompressible linear viscoelastic fluids in two-dimensional subject to periodic boundary condition and driven by random external forces. To do so we distinguish two cases, and for each case a global existence result of probabilistic weak solution is expounded in this paper. We also prove that under suitable hypotheses on the external random forces the solution turns out to be unique. As concrete examples, we consider the stochastic equations for the Maxwell and Oldroyd fluids that are of great importance in the investigation towards the understanding of the elastic turbulence.