Function-Space Differential Equations Associated with a Stochastic Partial Differential Equation.

摘要

The present work deals with a random convective diffusion equation related to the turbulent transport theory in the presence of molecular diffusion. However the equation can only be regarded as an idealized mathematical model since the velocity field is a generalized Gaussian random field, which is physically unrealistic; under this assumption, it becomes possible to treat this problem rigorously. This and the previous studies have clearly demonstrated that the use of functional calculus is necessary and inevitable in seeking ultimate solutions to turbulence problems.