PROPAGATION OF OSCILLATIONS IN THE SOLUTIONS OF 1-D COMPRESSIBLE FLUID EQUATIONS

We study the propagation of initial oscillations in the solutions of one-dimensional inviscid gas dynamic equations and the compressible Navier-Stokes equations. Using multiple scale analysis, we derive the homogenized equations which take the form of an averaged system coupled with a dynamic cell-problem. We prove rigorous error estimates to justify the validity of these equations. We also show that the weak limits of the oscillatory solutions satisfy gas dynamic equations with an equation of state depending on the microstructure of the initial data.