Publishing house / Banach Center Publications / All volumes

Abstract

We consider the equations of isentropic gas dynamics in Lagrangian coordinates. We are interested in global interactions of large waves, and their relation to global solvability and well-posedness for large data. One of the main difficulties in this program is the possible occurrence of a vacuum, in which the specific volume is infinite. In this paper we show that the vacuum cannot be generated in finite time. More precisely, if the vacuum is present for some positive time, then it must be present in the initial data, in a precise sense which is given. We also discuss the annihilation of vacuums that are present in the initial data.