On a certain class of singular solutions for power-law fluids

Abstrakt

We consider selfsimilar solutions to the power-law model for the incompressible fluids. The model reduces for $p=2$ to the Navier--Stokes equations.

For $p \in (1,\frac 32)$, we construct a class of selfsimilar solutions that are singular on a line passing through the origin. Further, we discuss singular solutions to the power-law fluid model without the convective term which are singular at one point.