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We carry out enhanced symmetry analysis of a two-dimensional Burgers system.The complete point symmetry group of this system is found using an enhancedversion of the algebraic method. Lie reductions of the Burgers system arecomprehensively studied in the optimal way and new Lie invariant solutions areconstructed. We prove that this system admits no local conservation laws andthen study hidden conservation laws, including potential ones. Various kinds ofhidden symmetries (continuous, discrete and potential ones) are considered forthis system as well. We exhaustively describe the solution subsets of theBurgers system that are its common solutions with its inviscid counterpart andwith the two-dimensional Navier-Stokes equations. Using the method ofdifferential constraints, which is particularly efficient for the Burgerssystem, we construct a number of wide families of solutions of this system thatare expressed in terms of solutions of the (1+1)-dimensional linear heatequation although they are not related to the well-known linearizable solutionsubset of the Burgers system.

Enhanced symmetry analysis of two-dimensional Burgers system