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

Abstract

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.

Keywords

• certain
• class
• singular
• solutions
• power-law
• fluids