DO SINGULAR STRUCTURES MOVE WITH AN INVISCID FLUID

Starting with analysis of a simple case of the inviscid Burgers equati on, we raise the question of the title as a fundamental characterizati on of general inviscid fluid motion. In particular, formation of high vorticity-gradient regions in two-dimensional Euler flow is studied nu merically both in physical space and in the Lagrangian marker space. E ach singular structure is shown to be fixed in the marker space for so me time, even though the strain and the vorticity gradient are not cle arly separated in scale.