On Global Large Solutions to 1-D Gas Dynamics.

We consider the 1-D Euler system (1)-(3) describing conservation of mass, momentum, and energy in compressible gas flow. For data with sufficiently small total variation Glimm's theorem [7] guarantees the existence of a global-in-time weak entropy admissible solution. The solution can be constructed by various methods: the Glimm scheme [7, 10], wave front-tracking [3], semidiscrete schemes [1], or vanishing viscosity [2]. The Euler system plays a distinguished role in the class of general conservation laws and much effort has been invested in extending Glimm's result to larger classes of data. for generic data the solution of the Euler equations is exceedingly complicated with a myriad of interactions resulting in complicated wave patterns. [ABSTRACT FROM AUTHOR]