Self-Similar Analytic Solution of the Two-Dimensional Navier-Stokes Equation with a Non-Newtonian Type of Viscosity

Abstract

We investigate Navier-Stokes (NS) and the continuity equations in Cartesian coordinates and Eulerian description for the two dimensional incompressible non-Newtonian fluids. Due to the non-Newtonian viscosity we consider the Ladyzenskaya model with a non-linear velocity dependent stress tensor. The key idea is the multidimensional generalization of the well-known self-similar Ansatz, which has already been used for non-compressible and compressible viscous flow studies. Geometrical interpretations of the trial function are also discussed. Our recent results are compared to the former Newtonian ones.

Keywords:

• self-similar solution
• Ladyzenskaya model
• non-Newtonian fluid

AMS Subject Classification:

• 34B09
• 35Q30