ABSTRACT
This chapter presents several more examples to show a wider range of applicability of the general results of stochastic partial differential equations. A major source of applications for stochastic partial differential equations comes from the statistical theory of turbulence in fluid dynamics and the related problems. All the examples presented are given in this area, even though there are other applications, such as in biology and systems science. The chapter studies the stochastic Burgers’ equation, as a simple model in turbulence, by means of a Hopf transformation. It analyses the mild solution of the Schrödinger equation with a random potential and elucidates the connection of the solution to the problem of wave propagation in random media. Finally, the chapter deals with the model equations for turbulence i.e. the randomly forced Navier-Stokes equations.
