Lie group analysis, exact solutions and conservation laws to compressible isentropic Navier–Stokes equation

The current study dedicated to the compressible isentropic Navier–Stokes equations in one-dimensional with a general pressure law. The Lie Group method is employed to reduce the compressible Navier–Stokes equations to a system of highly nonlinear ordinary differential equations with suitable similarity transformations. Consequently, with the help of exact solutions of reduced ordinary differential equations, similarity variable and similarity solutions, exact solutions of the main equation are obtained. Finally, using conservation laws multiplier, we find the complete set of local conservation laws of compressible isentropic Navier–Stokes equations for the arbitrary constant coefficients.