| Although the fundamental equations of fluid dynamics were derived a century or so ago, the role played by randomness in the movement of fluids has begun to be analysed only in recent years with the advent of the theory of stochastic differential equations (SDE's). This theory provides us with the tools and techniques needed for a rigorous investigation of hydrodynamical phenomena.; A central theme of this work is the investigation of the motion of point vortices. The basic quantity of interest is the stochastic vorticity signed measure . The use of the Skorohod-Ito SDE's enables us to incorporate in our framework the discontinuities inherent in this motion. A “jump-type”, (signed) measure-valued, nonlinear SDE for is derived and its unique solution is obtained under appropriate conditions. A continuous diffusion approximation to the solution is also given. |
