صندلی اداری

LIE GROUP ANALYSIS OF THE NAVIER-STOKES EQUATIONS IN THE POLAR CO-ORDINATES

K. Fakhar, S. Rani, Z.-C. Chen

Abstract


The equations of motion of two dimensional unsteady Navier-Stokesequations for viscous incompressible flow are written in polarco-ordinates. By employing Lie theory, the full one-parameterinfinitesimal transformation group leaving the equations of motioninvariant is derived along with its associated Lie algebra.Subgroups of the full group are then used to obtain a reduction byone in the number of independent variable in the system. Thesereductions are continued until a system of ordinary differentialequations is reached. An exact and a series type approximatesolutions of these ordinary differential equations are obtainedwhich lead to an exact and a series type approximate solutions in$ R^2 \setminus\{0\} $ to momentum equations.

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