Joint probability density of a passive article with force and magnetic field

Abstract: We firstly study the Navier-Stokes equation for the motion of a passive particle with harmonic, viscous, perturbative forces, subject to an exponentially correlated Gaussian force. Secondly, from the Fokker-Planck equation in an incompressible conducting fluid of magnetic field, we approximately obtain the solution of the joint probability density by using double Fourier transforms in three-time domains. In addition, the kurtosis, the correlation coefficient, and the moment from moment equation are numerically calculated.