Recent Mathematical Treatments of Laminar Flow and Transition Problems

Recent progress made in nonlinear stability theory of viscous, incompressible flows is discussed. First, progress made by means of the energy method is considered. In some cases the stability bounds obtained with the energy method coincide or nearly coincide with the critical values given by the linear stability theory. Further, a survey of recent mathematical investigations on the branching of steady solutions at the critical Reynolds (or Rayleigh) numbers is given. Finally, numerical methods solving the steady Navier—Stokes equations by finite differences are briefly mentioned.