Particles, vortex dynamics and stochastic partial differential equations

Abstract

The derivation of quasilinear stochastic partial differential equations (SPDE’s) for mass distributions and their generalizations is reviewed in Section 2. Special emphasis is given to the vorticity distribution and its macroscopic limit in a 2D-fluid. In Section 4 and 5 bilinear SPDE’s on weighted Hilbert spaces are derived from the underlying particle system. Moreover, it is shown that spatially homogeneous initial conditions imply that the solution is also spatially homogeneous. I.e., (non-Gaussian!!) homogeneous random fields are derived from an underlying particle system using SPDE methods.