Long Time Existence of Entropy Solutions to the One-Dimensional Non-isentropic Euler Equations with Periodic Initial Data

The non-isentropic Euler system with periodic initial data in R-1 is studied by analyzing wave interactions in a framework of specially chosen Riemann invariants, generalizing Glimm's functionals and applying the method of approximate conservation laws and approximate characteristics. An O(epsilon(-2)) lower bound is established for the life span of the entropy solutions with initial data that possess e variation in each period.