Some similarity solutions of the Navier-Stokes equations and related topics (Q1571112)

The authors consider the equation \[ f_{txx}+ ff_{xxx}- af_x f_{xx}= \nu f_{xxxx} \] together with suitable boundary and initial conditions. The equation arises e.g. in the context of two-dimensional Navier-Stokes flow, if one tries to find a stream function of the form \(\psi(x,y,t)= yf(x,t)\). The main results concern global existence and finite time blow up of solutions for various choices of the parameters \(a\in\mathbb{R}\) and \(\nu\geq 0\).