Initial value problem for the nonconservative zero-pressure gas dynamics system

Abstract

In this article, we study initial value problem for the zero-pressure gas dynamics system in non conservative form and the associated adhesion approximation. We use adhesion approximation and modi-ed adhesion approximation in the construction of weak asymptotic solution. First we prove a general existence result for the adhesion model for the initial velocity component in $$$H^s \mbox{ for } s$$$ > $$$ \frac{n}{2} + 1$$$ and the initial data for the density component being a $$$C^1$$$ function. Using this, we construct weak asymptotic solution for the system with initial velocity in $$$L^2 \cap L^{\infty}$$$ and the initial density being a bounded Borel measure. Then we make a detailed analysis of the explicit formula for the weak asymptotic solution and generalized solution for the plane-wave type initial data.