Lecture: Three-dimensional Fluid Motion and Long Compositions of Three-dimensional Volume Preserving Mappings

Dennis Parnell Sullivan

The calculus equations for the evolving volume preserving fluid motion in three-dimensional space are known practically to work very well for predicting the future behavior. This is also true theoretically, except the length of the time interval for theoretical predictions is limited by the initial conditions. Perhaps the evolution of some very smooth initial conditions blows up in finite time. This mystery is longstanding. The lecture will explore this mystery by studying long compositions of theoretical fluid motions for tiny intervals of time.

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