An existence theorem in the large for zero-pressure gas dynamics

Abstract

We obtain existence of a weak solution of the equations of zero-pressure gas dynamics, in any number of space dimensions plus time, given initial data of finite mass and kinetic energy. Our solution satisfies the "sticky particle" or adhesion dynamics conditions. The argument depends on a definition of a weak solution based on the introduction of Lagrangian coordinates and in particular on an application of the entropy condition proposed by C. Dafermos for hyperbolic systems of conservation laws.