The Cartesian analytical solutions for the N-dimensional compressible Navier–Stokes equations with density-dependent viscosity

In this paper, we prove the existence of general Cartesian vector solutions u = b ( t ) + A ( t ) x for the N -dimensional compressible Navier–Stokes equations with density-dependent viscosity, based on the matrix and curve integration theory. Two exact solutions are obtained by solving the reduced systems.