Numerical Approximation of $\rho_t + div(\rho V) = 0$

Noel J. Walkington
Department of Mathematical Sciences  
Carnegie Mellon University           

Abstract: 
The equation representing the balance of mass is a first order,
linear, homogeneous, hyperbolic equation. The theory for this
elementary equation becomes subtle when the velocity $V$ has
low regularity; for example, solutions of the Navier Stokes
equations with variable density and viscosity only lie in 
$L^2[0,T;H_0^1(\Omega)]$. This talk will give an overview of
the theory developed in 1989 by DiPerna and P. L. Lions for this 
equation. This theory will then be used to establish strong convergence
of DG schemes to approximate solutions.