Reduction of Nonlinear Problems to Schroedinger or Heat Equations: Formation of Kepler Orbits, Singular Solutions for Hydrodynamical Equations

摘要

A Newtonian diffusion model is applied to the formation of planetary orbits. A Navier-Stokes dissipative equation, whose solutions can be found by reduction to the linear heat equation by a transformation for going from the nonlinear equations for stochastic velocities (equivalent to the stochastic equation for the position process) to the Schroedinger equation for the quantities associated with the distribution of the process, is outlined. The solutions give velocity fields which are singular on the nodal surfaces of the solutions of the heat equation.