Approximately invariant solutions of creeping flow equations

Abstract

In this paper, the steady creeping flow equations of a second grade fluid in cartesian coordinates are considered; the equations involve a small parameter related to the dimensionless non--Newtonian coefficient. According to a recently introduced approach, the first order approximate Lie symmetries of the equations are computed, some classes of approximately invariant solutions are explicitly determined, and a boundary value problem is analyzed. The main aim of the paper is methodological, and the considered mechanical model is used to test the reliability of the procedure in a physically important application.

arXiv comment29 pages, no figures

References in corpus (3)

• A Consistent Approach to Approximate Lie Symmetries of Differential Equations
• Nonlinear first order PDEs reducible to autonomous form polynomially homogeneous in the derivatives
• Nonlinear first order partial differential equations reducible to first order homogeneous and autonomous quasilinear ones

Cited by in corpus (4)

• Approximate Noether symmetries of perturbed Lagrangians and approximate conservation laws
• Consistent approximate Q-conditional symmetries of PDEs: application to a hyperbolic reaction-diffusion-convection equation
• Approximate Q-conditional symmetries of partial differential equations
• Direct approach to approximate conservation laws