Systems of conservation laws in higher space dimensions

The existing paradox between theory and computational experiment for weak solutions of systems of conservation laws in higher space dimensions is arguably resolved. Apparently successful computations are identified with underlying boundary-value problems which are well-posed only in a weakened sense. In the absence of hyperbolicity in particular, prescribed boundary data sufficient to determine an a priori bound for an entropy weak solution need not suffice to imply local uniqueness thereof. In this context, fluid flow models based on stationary or self-similar reductions of Euler systems are distinguished as particularly attractive for computational investigation.