The Existence Theorems for Cauchy Problem to One Dimensional Models of Gas Dynamics

The paper studies the (2*2) system of equations to isentropic gas dynamics and the (3*3) one to full gas dynamics in Eulerian coordinates in one dimension. With the aid of Glimm's scheme the existence theorem is proved in the case of initial data have bounded variation. The proof uses only general properties of hyperbolic conservation laws and maximum principle, but is valid for strictly positive density and energy. It is also shown that Cauchy problem for isentropic gas dynamics system in Lagrangian coordinates is incorrect in the class of distributions.