Shock-free Solutions of the Compressible Euler Equations
  We study the structure of shock-free solutions of the compressible Euler equations with large data. We describe conditions under which the Rarefactive/Compressive character of solutions changes, and conditions under which the vacuum is formed asymptotically. We present several new examples of shock-free solutions, which demonstrate a large variety of behaviors. 
Geng Chen and Robin Young
math.AP