ABSTRACT
This chapter explains that the equations of the Prandtl system, which is the main object of investigation. It describes the main boundary value problems corresponding to various physical conditions of fluid dynamics. The chapter outlines some transformations of the variables commonly used for the examination of these problems. It discusses the separation of the boundary layer and the problem of closeness between the solutions of the Prandtl system and those of the Navier-Stokes system. The corresponding equations are written out for fluids with stresses expressed through powers of deformation velocities; in some sense, these equations generalize the Prandtl system. The Navier-Stokes equations are based on Newton's model of a viscous fluid. According to that model, tangential stresses in a fluid are linearly dependent on the respective shear deformation velocities. Magnetohydrodynamics (MHD) is a part of the modern theory of fluids that describes mixed hydrodynamic and electromagnetic processes arising in electrically conducting flows in the presence of magnetic fields.
