Unsteady 2D motions a viscous fluid described by partially invariant solutions to the Navier–Stokes equations

3D continuous subalgebra is used to searching partially invariant solution of viscous incompressible fluid equations. It can be interpreted as a 2D motion of one or two immiscible fluids in plane channel. The arising initial boundary value problem for factor-system is an inverse one. Unsteady problem for creeping motions is solved by separating of variables method for one fluid or Laplace transformation method for two fluids.