Invariant solutions of motion equations for ``power-law'' liquids (Q1115690)

The objective of this paper is to find all substantially different invariant solutions of the motion equations system for an incompressible viscous liquid with a ``powerlaw'' relation between stresses \(\tau_{ij}\) and deformation velocities \(e_{ij}\)- both in the full statement (*) \[ (\partial v_ t/\partial t)+v_ j(\partial v_ i/dx_ j)=(1/\rho)(\partial \tau_{ij}/\partial x_ j),\quad (\partial v_ i/\partial x_ i)=0, \] \[ \tau_{ij}=-p\delta_{ij}+2k| 2e_{ij}e_{ji}|^{(n-1)/2}e_{ij},\quad i,j=1-N, \] and in the boundary layer approximation (*), where k, n are rheologic parameters and N is the dimension of the physical space.