Progress Report on Contract N00014-93-1-0015 (University of Wisconsin)
Pagination or Media Count:
This effort concentrated in the study of self-similar viscous and fluid-dynamic limits. The invariance of hyperbolic systems of conservation laws under dilations of coordinates is a key property underlying much of the current theory. Viscous perturbations introduce an additional parabolic scale and this invariance is lost. Understanding how the two scales interact for small viscosities is an important step in the process of studying viscous limits for general solutions. One illuminating step in that direction is to consider the Riemann problem and to study artificial regularizations, rigged so as to preserve the invariance under dilations of coordinates and the entropy structure of the system. It provides information on how viscosity regularizes the whole wave fan emerging from Riemann data. At the technical level, it leads to study of singular perturbations for non-autonomous boundary-value problems, and the limiting process involves variation estimates.
- Fluid Mechanics