Conservation laws and Lie symmetries a (2+1)-dimensional thin film equation

This paper considers a generalized thin film equation in two spatial dimensions depending on three arbitrary functions. This equation describes the time evolution of a Newtonian liquid that is considerably thinner in one direction than in the other directions. We include a classification of point symmetries and the corresponding transformation groups. We derive all low-order local conservation laws of the equation in terms of the arbitrary functions. In addition, we discuss the physical meaning of the conserved quantities and provide a useful conservation identity.