Analytical solutions to the 1D compressible isothermal Navier–Stokes equations with Maxwell’s law

Abstract

In this paper, we present some analytical solutions to the one-dimensional compressible isothermal Navier–Stokes equations with Maxwell’s law in the real line. First, we construct two analytical solutions by using a self-similar ansatz, one blows up in finite time and the other exists globally-in-time. Second, we construct two global analytical solutions with different large initial data by using a non-self-similar ansatz.