Symmetry transformation of solutions for the Navier-Stokes equations

It is shown in this study that the Navier-Stokes equations allows an infinite-dimensional Lie group of symmetries, i.e., a group transforming solutions amongst each other. The Lie algebra of this symmetry group here depends on four arbitrary functions of time. Some new deformed solutions of Navier-Stokes equations in two and three-dimensions are obtained by applying some of the element of the symmetry group of these equations to their basic solutions. In order to explore the properties of deformed solutions, the analytic solutions are analyzed. It is noted that the corresponding deformed solutions behave as the basic solutions in the limiting sense for large time (i.e. t→∞).