On stochastic Euler equations
The authors consider equations for velocity fields describing compressible and incompressible motion of particles. The classical solutions for small time intervals are found. Next, the authors consider a uniform random perturbation of the position of individual particles \(X\) by a standard Brownian motion \(W\), i.e. \(\overline{X}(x,t)= X(x,t)+ \varepsilon W_t\). The velocity fields are solutions of the appropriate SPDE's (which are derived in the paper). It turns out that the limits, as \(\varepsilon \to 0\), are the deterministic velocity fields. For compressible motion a nonuniform random perturbation is considered.
scientific article; zbMATH DE number 1262943
scientific article