A group analysis of the 2D Navier–Stokes–Fourier equations

We study a (2+1)-dimensional model of an incompressible thermoconducting fluid named Navier–Stokes–Fourier system. We apply a group-theoretical analysis. In correspondence of the generators of the symmetry group allowed by this model, exact solutions are found. Some of them show possible interesting physical interpretations. In our first exploration, this feature is illustrated by dealing with simple special cases.