Equivalence of the Euler and Lagrangian equations of gas dynamics for weak solutions

摘要: Abstract This paper demonstrates the equivalence of Euler and Lagrangian equations gas dynamics in one space dimension for weak solutions which are bounded measurable Eulerian coordinates. The precise hypotheses include all known global on R × +. In particular, containing vacuum states (zero mass density) included. Furthermore, there is a one-to-one correspondence between convex extensions two systems, corresponding admissibility criteria equivalent. presence vacuum, definition solution must be strengthened to admit test functions discontinuous at vacuum. As an application, we translate large-data existence result DiPerna isentropic into similar theorem equations.